<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
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      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
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      background: transparent;
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      font-size: 0.68em;
      position: relative;
      top: -0.45em;
      margin-left: 1px;
      font-style: normal;
      font-weight: bold;
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      margin-left: 2px;
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      font-size: 1.18em;
      line-height: 1;
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      align-items: center;
      margin-right: -1px;
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      padding: 1px 3px 0 2px;
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      line-height: 1.1;
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      margin: 0 3px;
      font-weight: bold;
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      color: #b45309;
      font-weight: 700;
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      color: #475569;
      font-weight: 700;
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      align-items: center;
      gap: 6px;
      flex-shrink: 0;
      text-align: right;
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      font-size: 12px;
      font-weight: 600;
      padding: 3px 8px;
      border-radius: 6px;
      white-space: nowrap;
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      border: 1px solid #cbd5e1;
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      background: #eff6ff;
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      border-color: #bfdbfe;
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      background: #dcfce7;
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      font-size: 12px;
      font-weight: 700;
    }

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      .math-target {
        font-size: 18px;
      }
      .badge {
        font-size: 11px;
        padding: 2px 6px;
      }
      .step-row {
        padding: 8px 10px;
      }
      .left-col {
        gap: 8px;
      }
    }
  </style>
</head>
<body>
  <div class="stepper-wrap">
    <div class="controls">
      <div class="step-pills" role="tablist" aria-label="Step Navigation">
        <button class="pill-btn active" data-step="0" aria-label="Step 1">1</button>
        <button class="pill-btn" data-step="1" aria-label="Step 2">2</button>
        <button class="pill-btn" data-step="2" aria-label="Step 3">3</button>
        <button class="pill-btn" data-step="3" aria-label="Step 4">4</button>
      </div>
      <button class="play-btn" id="playBtn" aria-label="Toggle auto-play">
        <span id="playIcon">⏸</span> Pause
      </button>
    </div>

    <div class="steps-container">
      
      <div class="step-row active" data-step="0" tabindex="0" role="button" aria-label="Step 1: x squared equals 50, Original equation">
        <div class="left-col">
          <div class="step-num">1</div>
          <div class="math-target">
            <i>x</i><sup>2</sup>&nbsp;=&nbsp;50
          </div>
        </div>
        <div class="right-col">
          <span class="badge badge-gray">Original</span>
        </div>
      </div>

      
      <div class="step-row" data-step="1" tabindex="0" role="button" aria-label="Step 2: x equals plus minus square root of 50, Take square root">
        <div class="left-col">
          <div class="step-num">2</div>
          <div class="math-target">
            <i>x</i>&nbsp;=&nbsp;&plusmn;<span class="sqrt-group"><span class="sqrt-sym">&radic;</span><span class="radicand">50</span></span>
          </div>
        </div>
        <div class="right-col">
          <span class="badge badge-gray">Square Root</span>
        </div>
      </div>

      
      <div class="step-row" data-step="2" tabindex="0" role="button" aria-label="Step 3: x equals plus minus square root of 25 times 2, Factor largest perfect square">
        <div class="left-col">
          <div class="step-num">3</div>
          <div class="math-target">
            <i>x</i>&nbsp;=&nbsp;&plusmn;<span class="sqrt-group"><span class="sqrt-sym">&radic;</span><span class="radicand"><span class="gold-num">25</span><span class="dot">&middot;</span><span class="gray-num">2</span></span></span>
          </div>
        </div>
        <div class="right-col">
          <span class="badge badge-gray">Factor 25</span>
        </div>
      </div>

      
      <div class="step-row" data-step="3" tabindex="0" role="button" aria-label="Step 4: x equals plus minus 5 square root 2, Simplified exact form">
        <div class="left-col">
          <div class="step-num">4</div>
          <div class="math-target">
            <i>x</i>&nbsp;=&nbsp;&plusmn;<span class="gold-num">5</span><span class="sqrt-group"><span class="sqrt-sym">&radic;</span><span class="radicand"><span class="gray-num">2</span></span></span>
          </div>
        </div>
        <div class="right-col">
          <span class="badge badge-approx">≈ &plusmn;7.07</span>
        </div>
      </div>
    </div>
  </div>

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</body>
</html>

Solving Quadratic Equations of the Form x² = k

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Solving Quadratic Equation by Isolation</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      width: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #0f172a;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 10px 8px;
    }
    .flow-container {
      width: 100%;
      max-width: 400px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 4px;
    }
    .nav-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      flex-wrap: wrap;
      gap: 5px;
      margin-bottom: 6px;
      width: 100%;
    }
    .step-btn {
      padding: 5px 10px;
      font-size: 12px;
      font-weight: 600;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #334155;
      border-radius: 16px;
      cursor: pointer;
      transition: background-color 0.2s ease, color 0.2s ease, border-color 0.2s ease;
    }
    .step-btn:hover {
      background: #e2e8f0;
    }
    .step-btn.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
    }
    .play-btn {
      padding: 5px 10px;
      font-size: 12px;
      font-weight: 600;
      border: 1px solid #94a3b8;
      background: #ffffff;
      color: #0f172a;
      border-radius: 16px;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
      transition: background-color 0.2s ease;
    }
    .play-btn:hover {
      background: #f1f5f9;
    }
    .eq-box {
      width: 100%;
      max-width: 320px;
      padding: 6px 12px;
      border-radius: 8px;
      background: #f8fafc;
      border: 1.5px solid #cbd5e1;
      text-align: center;
      font-size: 17px;
      font-weight: 700;
      color: #0f172a;
      transition: all 0.25s ease;
      min-height: 38px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-family: 'Cambria Math', 'Times New Roman', serif, system-ui;
      letter-spacing: 0.5px;
    }
    .eq-box.active-box {
      border-color: #0284c7;
      background: #f0f9ff;
      box-shadow: 0 0 0 2px rgba(2, 132, 199, 0.25);
    }
    .step-row {
      width: 100%;
      max-width: 320px;
      display: flex;
      flex-direction: column;
      align-items: center;
      opacity: 0.35;
      transition: opacity 0.3s ease;
      cursor: pointer;
    }
    .step-row.active {
      opacity: 1;
    }
    .step-row.highlighted .action-pill {
      box-shadow: 0 0 0 2px #0f172a;
    }
    .connector {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 2px;
      margin: 2px 0;
    }
    .arrow-line {
      width: 2px;
      height: 7px;
      background: #64748b;
    }
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      display: inline-flex;
      align-items: center;
      gap: 4px;
      padding: 3px 12px;
      border-radius: 16px;
      font-size: 12px;
      font-weight: 700;
      color: #ffffff;
      transition: box-shadow 0.2s ease;
    }
    .pill-blue {
      background: #1d4ed8; /* High contrast: 6.2:1 with white */
    }
    .pill-purple {
      background: #6d28d9; /* High contrast: 6.4:1 with white */
    }
    .pill-teal {
      background: #0f766e; /* High contrast: 5.7:1 with white */
    }
    .arrow-down {
      width: 0;
      height: 0;
      border-left: 5px solid transparent;
      border-right: 5px solid transparent;
      border-top: 6px solid #64748b;
    }
    .check-section {
      width: 100%;
      max-width: 340px;
      margin-top: 4px;
      padding: 7px 10px;
      border-radius: 8px;
      background: #ecfdf5;
      border: 1.5px solid #6ee7b7;
      display: flex;
      flex-direction: column;
      gap: 4px;
      opacity: 0.35;
      transition: opacity 0.3s ease;
      cursor: pointer;
    }
    .check-section.active {
      opacity: 1;
    }
    .check-title {
      font-size: 11px;
      font-weight: 800;
      color: #065f46;
      display: flex;
      align-items: center;
      gap: 4px;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }
    .check-grid {
      display: flex;
      flex-direction: column;
      gap: 3px;
    }
    .check-item {
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding: 3px 8px;
      background: #ffffff;
      border-radius: 5px;
      border: 1px solid #a7f3d0;
      font-size: 13px;
      font-weight: 600;
      color: #064e3b;
      font-family: 'Cambria Math', 'Times New Roman', serif, system-ui;
    }
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      display: inline-flex;
      align-items: center;
      justify-content: center;
      width: 17px;
      height: 17px;
      border-radius: 50%;
      background: #059669;
      color: #ffffff;
      font-size: 11px;
      font-weight: bold;
      margin-left: 6px;
      flex-shrink: 0;
    }
    .math-sym {
      font-family: inherit;
    }
    sup {
      font-size: 0.75em;
      line-height: 0;
      position: relative;
      vertical-align: baseline;
      top: -0.45em;
    }
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        font-size: 15px;
        padding: 5px 8px;
      }
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        font-size: 11px;
        padding: 2px 9px;
      }
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        font-size: 11.5px;
        padding: 2px 6px;
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      .step-btn, .play-btn {
        font-size: 11px;
        padding: 3px 7px;
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  </style>
</head>
<body>

  <div class="flow-container">
    <div class="nav-bar" role="toolbar" aria-label="Step navigation">
      <button id="playBtn" class="play-btn" aria-label="Auto play steps"><span id="playIcon">▶</span> Auto</button>
      <button class="step-btn" data-step="0">Start</button>
      <button class="step-btn" data-step="1">Step 1</button>
      <button class="step-btn" data-step="2">Step 2</button>
      <button class="step-btn" data-step="3">Step 3</button>
      <button class="step-btn" data-step="4">Check</button>
    </div>

    
    <div id="box0" class="eq-box active-box" title="Given Equation">
      <span class="math-sym">3<i>x</i><sup>2</sup> − 7 = 41</span>
    </div>

    
    <div id="step1" class="step-row" data-step="1">
      <div class="connector">
        <div class="arrow-line"></div>
        <div class="action-pill pill-blue">
          <span>+ 7 to both sides</span>
        </div>
        <div class="arrow-down"></div>
      </div>
      <div id="box1" class="eq-box">
        <span class="math-sym">3<i>x</i><sup>2</sup> = 48</span>
      </div>
    </div>

    
    <div id="step2" class="step-row" data-step="2">
      <div class="connector">
        <div class="arrow-line"></div>
        <div class="action-pill pill-purple">
          <span>÷ 3 on both sides</span>
        </div>
        <div class="arrow-down"></div>
      </div>
      <div id="box2" class="eq-box">
        <span class="math-sym"><i>x</i><sup>2</sup> = 16</span>
      </div>
    </div>

    
    <div id="step3" class="step-row" data-step="3">
      <div class="connector">
        <div class="arrow-line"></div>
        <div class="action-pill pill-teal">
          <span>Apply ±√ to both sides</span>
        </div>
        <div class="arrow-down"></div>
      </div>
      <div id="box3" class="eq-box">
        <span class="math-sym"><i>x</i> = ±4</span>
      </div>
    </div>

    
    <div id="checkSection" class="check-section">
      <div class="check-title">
        <span>✓ Verification</span>
      </div>
      <div class="check-grid">
        <div class="check-item">
          <span>3(4)<sup>2</sup> − 7 = 48 − 7 = 41</span>
          <span class="badge-check">✓</span>
        </div>
        <div class="check-item">
          <span>3(−4)<sup>2</sup> − 7 = 48 − 7 = 41</span>
          <span class="badge-check">✓</span>
        </div>
      </div>
    </div>
  </div>

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</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e293b;
      background: transparent;
      padding: 16px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      min-height: auto;
    }

    .title-banner {
      font-size: 18px;
      font-weight: 700;
      color: #0f172a;
      margin-bottom: 14px;
      text-align: center;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
    }

    .math-sym {
      font-family: 'Cambria Math', 'Times New Roman', serif;
      font-style: italic;
    }
    .math-sym sup {
      font-family: system-ui, -apple-system, sans-serif;
      font-style: normal;
      font-size: 0.75em;
      top: -0.4em;
    }

    .grid {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 12px;
      width: 100%;
      max-width: 620px;
    }

    @media (max-width: 520px) {
      .grid {
        grid-template-columns: 1fr;
        gap: 10px;
      }
    }

    .case-card {
      background: #ffffff;
      border-radius: 10px;
      padding: 14px 10px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      text-align: center;
      cursor: pointer;
      user-select: none;
      transition: background-color 0.2s ease, box-shadow 0.2s ease, border-color 0.2s ease;
      border: 1px solid #e2e8f0;
    }

    /* Green Card (k > 0) */
    .card-pos {
      border-top: 4px solid #16a34a;
    }
    .card-pos:hover, .card-pos.active {
      box-shadow: 0 0 0 2px #16a34a, 0 4px 12px rgba(22, 163, 74, 0.12);
      background: #f0fdf4;
    }
    .card-pos .badge {
      background: #dcfce7;
      color: #15803d;
    }
    .card-pos .count {
      color: #15803d;
    }
    .card-pos .solution-line {
      color: #16a34a;
    }

    /* Blue Card (k = 0) */
    .card-zero {
      border-top: 4px solid #0284c7;
    }
    .card-zero:hover, .card-zero.active {
      box-shadow: 0 0 0 2px #0284c7, 0 4px 12px rgba(2, 132, 199, 0.12);
      background: #f0f9ff;
    }
    .card-zero .badge {
      background: #e0f2fe;
      color: #0369a1;
    }
    .card-zero .count {
      color: #0369a1;
    }
    .card-zero .solution-line {
      color: #0284c7;
    }

    /* Red Card (k < 0) */
    .card-neg {
      border-top: 4px solid #dc2626;
    }
    .card-neg:hover, .card-neg.active {
      box-shadow: 0 0 0 2px #dc2626, 0 4px 12px rgba(220, 38, 38, 0.12);
      background: #fef2f2;
    }
    .card-neg .badge {
      background: #fee2e2;
      color: #b91c1c;
    }
    .card-neg .count {
      color: #b91c1c;
    }
    .card-neg .solution-line {
      color: #dc2626;
    }

    .badge {
      font-size: 14px;
      font-weight: 700;
      padding: 3px 12px;
      border-radius: 16px;
      margin-bottom: 6px;
      letter-spacing: 0.5px;
    }

    .count {
      font-size: 13px;
      font-weight: 700;
      margin-bottom: 8px;
      letter-spacing: -0.1px;
    }

    .example-box {
      width: 100%;
      background: rgba(255, 255, 255, 0.9);
      border: 1px dashed #cbd5e1;
      border-radius: 6px;
      padding: 8px 4px;
      margin-bottom: 8px;
      display: flex;
      flex-direction: column;
      gap: 3px;
      min-height: 52px;
      justify-content: center;
    }

    .example-eq {
      font-size: 14px;
      font-weight: 600;
      color: #334155;
    }

    .solution-line {
      font-weight: 700;
      font-size: 14px;
    }

    .note-text {
      font-size: 11px;
      font-weight: 500;
      color: #64748b;
      line-height: 1.2;
    }

    .axis-svg {
      width: 100%;
      height: 38px;
      margin-top: 2px;
    }
  </style>
</head>
<body>

  <div class="title-banner">
    Solving <span class="math-sym">x<sup>2</sup> = k</span>
  </div>

  <div class="grid">
    
    <div class="case-card card-pos active" onclick="selectCard(this)">
      <div class="badge"><span class="math-sym">k</span> &gt; 0</div>
      <div class="count">Two Real Solutions</div>
      <div class="example-box">
        <div class="example-eq"><span class="math-sym">x<sup>2</sup></span> = 9</div>
        <div class="solution-line"><span class="math-sym">x</span> = &plusmn;3</div>
      </div>
      <svg class="axis-svg" viewBox="0 0 160 36">
        
        <line x1="12" y1="20" x2="148" y2="20" stroke="#94a3b8" stroke-width="2" stroke-linecap="round"/>
        
        <line x1="80" y1="16" x2="80" y2="24" stroke="#94a3b8" stroke-width="1.5"/>
        <text x="80" y="33" font-size="10" text-anchor="middle" fill="#64748b">0</text>
        
        <circle cx="36" cy="20" r="4.5" fill="#16a34a" />
        <text x="36" y="11" font-size="10" font-weight="700" text-anchor="middle" fill="#15803d">-3</text>
        
        <circle cx="124" cy="20" r="4.5" fill="#16a34a" />
        <text x="124" y="11" font-size="10" font-weight="700" text-anchor="middle" fill="#15803d">+3</text>
      </svg>
    </div>

    
    <div class="case-card card-zero" onclick="selectCard(this)">
      <div class="badge"><span class="math-sym">k</span> = 0</div>
      <div class="count">One Real Solution</div>
      <div class="example-box">
        <div class="example-eq"><span class="math-sym">x<sup>2</sup></span> = 0</div>
        <div class="solution-line"><span class="math-sym">x</span> = 0</div>
      </div>
      <svg class="axis-svg" viewBox="0 0 160 36">
        
        <line x1="12" y1="20" x2="148" y2="20" stroke="#94a3b8" stroke-width="2" stroke-linecap="round"/>
        
        <circle cx="80" cy="20" r="5" fill="#0284c7" />
        <text x="80" y="11" font-size="10" font-weight="700" text-anchor="middle" fill="#0369a1">0</text>
      </svg>
    </div>

    
    <div class="case-card card-neg" onclick="selectCard(this)">
      <div class="badge"><span class="math-sym">k</span> &lt; 0</div>
      <div class="count">No Real Solutions</div>
      <div class="example-box">
        <div class="example-eq"><span class="math-sym">x<sup>2</sup></span> = &minus;9</div>
        <div class="solution-line" style="font-size:12px;">No real values</div>
      </div>
      <svg class="axis-svg" viewBox="0 0 160 36">
        
        <line x1="12" y1="20" x2="148" y2="20" stroke="#94a3b8" stroke-width="2" stroke-linecap="round"/>
        
        <line x1="80" y1="16" x2="80" y2="24" stroke="#94a3b8" stroke-width="1.5"/>
        <text x="80" y="33" font-size="10" text-anchor="middle" fill="#64748b">0</text>
        
        <text x="80" y="14" font-size="13" font-weight="700" text-anchor="middle" fill="#dc2626">&#8709;</text>
      </svg>
    </div>
  </div>

  <script>
    function selectCard(el) {
      document.querySelectorAll('.case-card').forEach(c => c.classList.remove('active'));
      el.classList.add('active');
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .header {
      font-size: 16px;
      font-weight: 700;
      letter-spacing: -0.01em;
      margin-bottom: 12px;
      color: #1e2945;
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .grid {
      display: grid;
      grid-template-columns: repeat(2, 1fr);
      gap: 12px;
      width: 100%;
      max-width: 580px;
    }
    .panel {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 240px;
      box-shadow: 0 2px 6px rgba(0,0,0,0.04);
      transition: border-color 0.2s ease, box-shadow 0.2s ease;
      cursor: pointer;
      user-select: none;
    }
    .panel:hover, .panel.active {
      border-color: #3b82f6;
      box-shadow: 0 4px 12px rgba(59,130,246,0.12);
    }
    .panel-title {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      text-transform: uppercase;
      letter-spacing: 0.04em;
    }
    .geo-box {
      position: relative;
      width: 110px;
      height: 110px;
      background: #e0f2fe;
      border: 2px solid #0284c7;
      border-radius: 8px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-weight: 700;
      color: #0369a1;
      font-size: 15px;
      margin: 14px 0 6px;
    }
    .dim-label {
      position: absolute;
      font-size: 13px;
      font-weight: 600;
      color: #0284c7;
    }
    .dim-top { top: -20px; left: 50%; transform: translateX(-50%); }
    .dim-left { left: -20px; top: 50%; transform: translateY(-50%); }
    
    .tree-container {
      width: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      margin: 4px 0;
    }
    .root-node {
      background: #ffffff;
      border: 1.5px solid #cbd5e1;
      padding: 4px 12px;
      border-radius: 6px;
      font-weight: 700;
      font-size: 15px;
      color: #1e2945;
    }
    .branches-svg {
      width: 100%;
      height: 32px;
      max-width: 180px;
    }
    .branch-leaves {
      display: flex;
      justify-content: space-between;
      width: 100%;
      max-width: 220px;
      gap: 6px;
    }
    .leaf {
      flex: 1;
      background: #ffffff;
      border: 1.5px solid #cbd5e1;
      border-radius: 8px;
      padding: 6px 4px;
      text-align: center;
      font-size: 12px;
      line-height: 1.3;
      transition: all 0.2s ease;
    }
    .leaf.pos { border-color: #38bdf8; background: #f0f9ff; }
    .leaf.neg { border-color: #a855f7; background: #faf5ff; }
    .leaf-math {
      font-weight: 700;
      font-size: 13px;
      color: #1e2945;
    }
    .badge {
      font-size: 12px;
      font-weight: 600;
      padding: 4px 10px;
      border-radius: 20px;
      margin-top: 4px;
    }
    .badge-geo { background: #e0f2fe; color: #0369a1; }
    .badge-alg { background: #f3e8ff; color: #7e22ce; }

    @media (max-width: 420px) {
      .geo-box { width: 90px; height: 90px; }
      .leaf-math { font-size: 12px; }
      .dim-top { top: -18px; }
      .dim-left { left: -18px; }
    }
  </style>
</head>
<body>

  <div class="header">Two Roads to 36</div>

  <div class="grid">
    
    <div class="panel active" id="geoCard">
      <div class="panel-title">Geometry (Lengths)</div>
      
      <div class="geo-box">
        <span class="dim-label dim-top">6</span>
        <span class="dim-label dim-left">6</span>
        Area = 36
      </div>

      <div class="badge badge-geo">1 solution: <i>x</i> = 6</div>
    </div>

    
    <div class="panel active" id="algCard">
      <div class="panel-title">Algebra (All Reals)</div>
      
      <div class="tree-container">
        <div class="root-node"><i>x</i>² = 36</div>
        
        <svg class="branches-svg" viewBox="0 0 160 30">
          <path d="M 80 0 L 80 8 L 30 8 L 30 26" fill="none" stroke="#94a3b8" stroke-width="2" />
          <path d="M 80 0 L 80 8 L 130 8 L 130 26" fill="none" stroke="#94a3b8" stroke-width="2" />
          <polygon points="30,30 26,22 34,22" fill="#94a3b8" />
          <polygon points="130,30 126,22 134,22" fill="#94a3b8" />
        </svg>

        <div class="branch-leaves">
          <div class="leaf pos">
            <div class="leaf-math">(+6)² = 36</div>
            <div style="color:#0284c7;font-weight:600;font-size:11px;"><i>x</i> = +6</div>
          </div>
          <div class="leaf neg">
            <div class="leaf-math">(-6)² = 36</div>
            <div style="color:#7e22ce;font-weight:600;font-size:11px;"><i>x</i> = -6</div>
          </div>
        </div>
      </div>

      <div class="badge badge-alg">2 solutions: <i>x</i> = ±6</div>
    </div>
  </div>

  <script>
    const geo = document.getElementById('geoCard');
    const alg = document.getElementById('algCard');

    function toggleFocus(activeCard, otherCard) {
      activeCard.classList.add('active');
      otherCard.classList.remove('active');
    }

    geo.addEventListener('click', () => toggleFocus(geo, alg));
    alg.addEventListener('click', () => toggleFocus(alg, geo));
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      user-select: none;
    }

    body {
      width: 100%;
      min-height: 100%;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 12px 10px;
    }

    /* Toggle bar */
    .toggle-row {
      display: flex;
      gap: 6px;
      background: #f1f5f9;
      padding: 3px;
      border-radius: 20px;
      margin-bottom: 8px;
    }

    .toggle-btn {
      border: none;
      background: transparent;
      padding: 4px 14px;
      border-radius: 16px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      transition: all 0.25s ease;
    }

    .toggle-btn.active {
      background: #ffffff;
      color: #0f172a;
      box-shadow: 0 1px 4px rgba(0, 0, 0, 0.1);
    }

    /* Diagram Area */
    .diagram-area {
      position: relative;
      width: 100%;
      max-width: 360px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
      flex: 1;
      justify-content: center;
    }

    /* Node styles */
    .math-node {
      background: #ffffff;
      border: 2px solid #e2e8f0;
      border-radius: 12px;
      padding: 6px 16px;
      font-size: 19px;
      font-weight: 700;
      color: #0f172a;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
      z-index: 2;
      transition: transform 0.2s ease, border-color 0.2s ease;
    }

    .top-node {
      border-color: #cbd5e1;
      background: #f8fafc;
      padding: 6px 20px;
      font-size: 20px;
    }

    /* Branch row */
    .branch-row {
      display: flex;
      width: 100%;
      justify-content: space-between;
      gap: 12px;
      position: relative;
    }

    .branch-col {
      flex: 1;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 4px;
      z-index: 2;
    }

    .branch-card {
      width: 100%;
      border-radius: 12px;
      padding: 8px 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 2px;
      transition: transform 0.2s ease, box-shadow 0.2s ease;
    }

    .branch-card.pos {
      background: #f0fdf9;
      border: 2px solid #22c7a9;
    }

    .branch-card.neg {
      background: #fff5f5;
      border: 2px solid #ff6b6b;
    }

    .branch-math {
      font-size: 18px;
      font-weight: 700;
    }

    .pos .branch-math { color: #0d9478; }
    .neg .branch-math { color: #e04848; }

    .tag {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.4px;
      padding: 2px 8px;
      border-radius: 6px;
    }

    .tag-pos {
      background: #22c7a9;
      color: #ffffff;
    }

    .tag-neg {
      background: #ff6b6b;
      color: #ffffff;
    }

    /* Combined Box */
    .combined-card {
      background: #f8fafc;
      border: 2px solid #94a3b8;
      border-radius: 14px;
      padding: 8px 18px;
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
      z-index: 2;
      width: 100%;
      max-width: 250px;
    }

    .combined-math {
      font-size: 22px;
      font-weight: 800;
      color: #0f172a;
      letter-spacing: 0.5px;
    }

    .pm-symbol {
      display: inline-block;
      padding: 0 2px;
      position: relative;
    }

    .pm-callout {
      display: flex;
      align-items: center;
      gap: 6px;
      margin-top: 4px;
      font-size: 12px;
      font-weight: 600;
      color: #475569;
      background: #ffffff;
      padding: 3px 10px;
      border-radius: 8px;
      border: 1px solid #cbd5e1;
    }

    .pm-callout span.p { color: #0d9478; font-weight: 800; }
    .pm-callout span.m { color: #e04848; font-weight: 800; }

    /* SVG Connecting Lines */
    .svg-lines {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: 100%;
      pointer-events: none;
      z-index: 1;
    }

    sup {
      font-size: 0.65em;
      line-height: 0;
      vertical-align: 0.45em;
    }

    .sqrt {
      white-space: nowrap;
    }
  </style>
</head>
<body>

  
  <div class="toggle-row">
    <button class="toggle-btn active" id="btnGen" onclick="setMode('gen')">Formula (k)</button>
    <button class="toggle-btn" id="btnEx" onclick="setMode('ex')">Example (36)</button>
  </div>

  
  <div class="diagram-area" id="diagram">
    <svg class="svg-lines" viewBox="0 0 340 250" preserveAspectRatio="none">
      
      <path d="M 170 36 C 170 68, 85 58, 85 92" fill="none" stroke="#22c7a9" stroke-width="2.5" stroke-dasharray="3 3"/>
      <path d="M 170 36 C 170 68, 255 58, 255 92" fill="none" stroke="#ff6b6b" stroke-width="2.5" stroke-dasharray="3 3"/>
      <polygon points="85,96 81,87 89,87" fill="#22c7a9"/>
      <polygon points="255,96 251,87 259,87" fill="#ff6b6b"/>

      
      <path d="M 85 152 C 85 174, 130 178, 145 186" fill="none" stroke="#22c7a9" stroke-width="2" stroke-linecap="round"/>
      <path d="M 255 152 C 255 174, 210 178, 195 186" fill="none" stroke="#ff6b6b" stroke-width="2" stroke-linecap="round"/>
    </svg>

    
    <div class="math-node top-node" id="nodeTop">
      x<sup>2</sup> = k
    </div>

    
    <div class="branch-row">
      
      <div class="branch-col">
        <div class="branch-card pos">
          <span class="tag tag-pos">Principal Root</span>
          <div class="branch-math" id="nodePos">x = +√k</div>
        </div>
      </div>

      
      <div class="branch-col">
        <div class="branch-card neg">
          <span class="tag tag-neg">Negative Root</span>
          <div class="branch-math" id="nodeNeg">x = −√k</div>
        </div>
      </div>
    </div>

    
    <div class="combined-card">
      <div class="combined-math" id="nodeComb">
        x = <span class="pm-symbol">±</span><span id="combVal">√k</span>
      </div>
      <div class="pm-callout">
        <span class="p">+</span> or <span class="m">−</span> (two solutions)
      </div>
    </div>
  </div>

  <script>
    function setMode(mode) {
      const isEx = mode === 'ex';
      
      document.getElementById('btnGen').classList.toggle('active', !isEx);
      document.getElementById('btnEx').classList.toggle('active', isEx);

      if (isEx) {
        document.getElementById('nodeTop').innerHTML = 'x<sup>2</sup> = 36';
        document.getElementById('nodePos').innerHTML = 'x = +6';
        document.getElementById('nodeNeg').innerHTML = 'x = −6';
        document.getElementById('nodeComb').innerHTML = 'x = <span class="pm-symbol">±</span>6';
      } else {
        document.getElementById('nodeTop').innerHTML = 'x<sup>2</sup> = k';
        document.getElementById('nodePos').innerHTML = 'x = +√k';
        document.getElementById('nodeNeg').innerHTML = 'x = −√k';
        document.getElementById('nodeComb').innerHTML = 'x = <span class="pm-symbol">±</span>√k';
      }
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>System of Equations: Point of Intersection</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e293b;
      background: transparent;
      padding: 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      user-select: none;
    }
    .main-wrap {
      width: 100%;
      max-width: 460px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }
    .graph-container {
      width: 100%;
      background: #f8fafc;
      border-radius: 8px;
      border: 1px solid #e2e8f0;
      position: relative;
      overflow: hidden;
    }
    svg {
      display: block;
      width: 100%;
      height: auto;
    }
    .grid-line {
      stroke: #e2e8f0;
      stroke-width: 1;
    }
    .axis-line {
      stroke: #94a3b8;
      stroke-width: 1.75;
    }
    .axis-label {
      font-size: 11px;
      font-weight: 600;
      fill: #64748b;
    }
    .tick-label {
      font-size: 10px;
      font-weight: 500;
      fill: #94a3b8;
      font-family: "SF Mono", Monaco, Consolas, monospace;
    }
    
    /* Interactive line styles */
    .plot-line {
      cursor: pointer;
      transition: stroke-width 0.2s ease, opacity 0.2s ease;
    }
    .line-purple {
      stroke: #8b5cf6;
      stroke-width: 3;
    }
    .line-teal {
      stroke: #0d9488;
      stroke-width: 3;
    }
    .line-dimmed {
      opacity: 0.25;
    }
    .line-active {
      stroke-width: 4.5;
      filter: drop-shadow(0 0 3px rgba(0,0,0,0.15));
    }

    /* Interactive point */
    .point-group {
      cursor: pointer;
    }
    .point-pulse {
      animation: pulse 2.2s infinite ease-out;
      transform-origin: 145px 90px;
    }
    @keyframes pulse {
      0% { r: 6px; opacity: 0.85; }
      70% { r: 16px; opacity: 0; }
      100% { r: 16px; opacity: 0; }
    }

    .boxes-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 8px;
      width: 100%;
    }
    .sub-box {
      padding: 8px 10px;
      border-radius: 8px;
      font-size: 13px;
      line-height: 1.35;
      display: flex;
      flex-direction: column;
      gap: 3px;
      cursor: pointer;
      transition: box-shadow 0.2s ease, border-color 0.2s ease, opacity 0.2s ease;
    }
    .sub-box:hover {
      box-shadow: 0 2px 6px rgba(0,0,0,0.06);
    }
    .box-purple {
      background: #f5f3ff;
      border: 1.5px solid #c4b5fd;
      color: #5b21b6;
    }
    .box-teal {
      background: #f0fdfa;
      border: 1.5px solid #99f6e4;
      color: #0f766e;
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    .box-active {
      border-width: 2px;
      box-shadow: 0 0 0 2px rgba(99, 102, 241, 0.2);
    }
    .box-dimmed {
      opacity: 0.4;
    }

    .eq-head {
      font-weight: 700;
      font-size: 13.5px;
      display: flex;
      justify-content: space-between;
      align-items: center;
    }
    .math-step {
      font-family: "SF Mono", Monaco, Consolas, monospace;
      font-size: 12px;
      color: #334155;
      background: rgba(255, 255, 255, 0.6);
      padding: 2px 4px;
      border-radius: 4px;
    }
    .check-row {
      font-weight: 700;
      font-size: 12.5px;
      display: flex;
      align-items: center;
      gap: 4px;
      margin-top: 1px;
    }
    .check-purple { color: #7c3aed; }
    .check-teal { color: #0d9488; }

    .banner {
      width: 100%;
      background: #ecfdf5;
      border: 1.5px solid #a7f3d0;
      color: #065f46;
      border-radius: 8px;
      padding: 6px 10px;
      font-size: 13px;
      font-weight: 700;
      text-align: center;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      cursor: pointer;
      transition: background-color 0.2s ease, border-color 0.2s ease;
    }
    .banner:hover {
      background: #d1fae5;
    }
    .var-x {
      color: #2563eb;
      font-weight: 700;
    }
    .var-y {
      color: #d97706;
      font-weight: 700;
    }

    .graph-badge {
      cursor: pointer;
    }
  </style>
</head>
<body>

<div class="main-wrap">
  
  <div class="graph-container">
    
    <svg viewBox="0 0 360 210" aria-label="Coordinate plane showing intersection of y = x + 1 and y = -2x + 4 at (1, 2)">
      
      <g class="grid-line">
        
        <line x1="40" y1="12" x2="40" y2="200" />
        <line x1="75" y1="12" x2="75" y2="200" />
        <line x1="145" y1="12" x2="145" y2="200" />
        <line x1="180" y1="12" x2="180" y2="200" />
        <line x1="215" y1="12" x2="215" y2="200" />
        <line x1="250" y1="12" x2="250" y2="200" />
        <line x1="285" y1="12" x2="285" y2="200" />
        <line x1="320" y1="12" x2="320" y2="200" />

        
        <line x1="20" y1="20" x2="345" y2="20" />
        <line x1="20" y1="55" x2="345" y2="55" />
        <line x1="20" y1="90" x2="345" y2="90" />
        <line x1="20" y1="125" x2="345" y2="125" />
        <line x1="20" y1="195" x2="345" y2="195" />
      </g>

      
      
      <line x1="18" y1="160" x2="346" y2="160" class="axis-line" />
      <polygon points="351,160 343,156.5 343,163.5" fill="#94a3b8" />
      <text x="353" y="164" class="axis-label">x</text>

      
      <line x1="110" y1="202" x2="110" y2="14" class="axis-line" />
      <polygon points="110,9 106.5,17 113.5,17" fill="#94a3b8" />
      <text x="110" y="7" class="axis-label" text-anchor="middle">y</text>

      
      <text x="75" y="174" class="tick-label" text-anchor="middle">-1</text>
      <text x="101" y="174" class="tick-label" text-anchor="end">0</text>
      <text x="145" y="174" class="tick-label" text-anchor="middle">1</text>
      <text x="180" y="174" class="tick-label" text-anchor="middle">2</text>
      <text x="215" y="174" class="tick-label" text-anchor="middle">3</text>
      <text x="250" y="174" class="tick-label" text-anchor="middle">4</text>
      <text x="285" y="174" class="tick-label" text-anchor="middle">5</text>

      
      <text x="98" y="198" class="tick-label" text-anchor="end">-1</text>
      <text x="98" y="128" class="tick-label" text-anchor="end">1</text>
      <text x="98" y="93" class="tick-label" text-anchor="end">2</text>
      <text x="98" y="58" class="tick-label" text-anchor="end">3</text>
      <text x="98" y="23" class="tick-label" text-anchor="end">4</text>

      
      
      <line id="svgLine1" x1="33" y1="202" x2="225.5" y2="9.5" class="plot-line line-purple" stroke-linecap="round" />

      
      
      <line id="svgLine2" x1="103" y1="6" x2="197.5" y2="195" class="plot-line line-teal" stroke-linecap="round" />

      
      <g id="badgeLine1" class="graph-badge" transform="translate(218, 16)">
        <rect x="0" y="0" width="76" height="20" rx="4" fill="#f5f3ff" stroke="#c4b5fd" stroke-width="1.2" />
        <text x="38" y="14" font-size="11" font-weight="700" fill="#6d28d9" text-anchor="middle">y = x + 1</text>
      </g>

      
      <g id="badgeLine2" class="graph-badge" transform="translate(22, 28)">
        <rect x="0" y="0" width="82" height="20" rx="4" fill="#f0fdfa" stroke="#99f6e4" stroke-width="1.2" />
        <text x="41" y="14" font-size="11" font-weight="700" fill="#0f766e" text-anchor="middle">y = -2x + 4</text>
      </g>

      
      <g id="pointGroup" class="point-group">
        
        <circle cx="145" cy="90" r="6" fill="none" stroke="#f59e0b" stroke-width="2" class="point-pulse" />
        
        <circle cx="145" cy="90" r="5.5" fill="#f59e0b" stroke="#ffffff" stroke-width="2" />

        
        <g transform="translate(156, 78)">
          <rect x="0" y="0" width="52" height="22" rx="4" fill="#ffffff" stroke="#f59e0b" stroke-width="1.5" />
          <text x="26" y="15" font-size="12" font-weight="700" fill="#b45309" text-anchor="middle">(1, 2)</text>
        </g>
      </g>
    </svg>
  </div>

  
  <div class="boxes-grid">
    
    <div class="sub-box box-purple" id="boxLine1">
      <div class="eq-head">
        <span>Line 1: y = x + 1</span>
      </div>
      <div class="math-step">
        (<span class="var-y">2</span>) = (<span class="var-x">1</span>) + 1
      </div>
      <div class="check-row check-purple">
        <span>2 = 2</span>
        <span>✓</span>
      </div>
    </div>

    
    <div class="sub-box box-teal" id="boxLine2">
      <div class="eq-head">
        <span>Line 2: y = -2x + 4</span>
      </div>
      <div class="math-step">
        (<span class="var-y">2</span>) = -2(<span class="var-x">1</span>) + 4
      </div>
      <div class="check-row check-teal">
        <span>2 = 2</span>
        <span>✓</span>
      </div>
    </div>
  </div>

  
  <div class="banner" id="bannerBtn">
    <span>✓</span>
    <span>(1, 2) makes BOTH equations true!</span>
  </div>
</div>

<script>
  let activeFocus = null; // 'line1', 'line2', 'both', or null

  const line1 = document.getElementById('svgLine1');
  const line2 = document.getElementById('svgLine2');
  const badge1 = document.getElementById('badgeLine1');
  const badge2 = document.getElementById('badgeLine2');
  const box1 = document.getElementById('boxLine1');
  const box2 = document.getElementById('boxLine2');
  const pt = document.getElementById('pointGroup');
  const banner = document.getElementById('bannerBtn');

  function updateHighlight() {
    if (activeFocus === 'line1') {
      line1.classList.add('line-active');
      line1.classList.remove('line-dimmed');
      line2.classList.remove('line-active');
      line2.classList.add('line-dimmed');

      box1.classList.add('box-active');
      box1.classList.remove('box-dimmed');
      box2.classList.remove('box-active');
      box2.classList.add('box-dimmed');
    } else if (activeFocus === 'line2') {
      line2.classList.add('line-active');
      line2.classList.remove('line-dimmed');
      line1.classList.remove('line-active');
      line1.classList.add('line-dimmed');

      box2.classList.add('box-active');
      box2.classList.remove('box-dimmed');
      box1.classList.remove('box-active');
      box1.classList.add('box-dimmed');
    } else if (activeFocus === 'both') {
      line1.classList.add('line-active');
      line1.classList.remove('line-dimmed');
      line2.classList.add('line-active');
      line2.classList.remove('line-dimmed');

      box1.classList.add('box-active');
      box1.classList.remove('box-dimmed');
      box2.classList.add('box-active');
      box2.classList.remove('box-dimmed');
    } else {
      line1.classList.remove('line-active', 'line-dimmed');
      line2.classList.remove('line-active', 'line-dimmed');
      box1.classList.remove('box-active', 'box-dimmed');
      box2.classList.remove('box-active', 'box-dimmed');
    }
  }

  function toggleFocus(type) {
    activeFocus = activeFocus === type ? null : type;
    updateHighlight();
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  line1.addEventListener('click', () => toggleFocus('line1'));
  badge1.addEventListener('click', () => toggleFocus('line1'));
  box1.addEventListener('click', () => toggleFocus('line1'));

  line2.addEventListener('click', () => toggleFocus('line2'));
  badge2.addEventListener('click', () => toggleFocus('line2'));
  box2.addEventListener('click', () => toggleFocus('line2'));

  pt.addEventListener('click', () => toggleFocus('both'));
  banner.addEventListener('click', () => toggleFocus('both'));
</script>

</body>
</html>

Understanding Systems of Equations as Points of Intersection

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      user-select: none;
    }
    .layout {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      align-items: center;
    }
    @media (max-width: 520px) {
      .layout {
        grid-template-columns: 1fr;
      }
    }
    .graph-container {
      background: #f8fafc;
      border-radius: 12px;
      padding: 8px;
      display: flex;
      justify-content: center;
      align-items: center;
    }
    svg {
      width: 100%;
      max-width: 280px;
      height: auto;
      overflow: visible;
    }
    .tabs {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 6px;
    }
    .tab-btn {
      border: 2px solid #e2e8f0;
      background: #f8fafc;
      color: #64748b;
      padding: 8px 4px;
      border-radius: 8px;
      font-weight: 700;
      font-size: 14px;
      cursor: pointer;
      text-align: center;
      transition: all 0.2s ease;
    }
    .tab-btn.active {
      border-color: #22b7ff;
      background: #eff6ff;
      color: #1e2945;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.2);
    }
    .eval-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }
    .eq-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding: 8px 10px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
    }
    .eq-blue {
      background: #eff6ff;
      border-left: 4px solid #2563eb;
      color: #1e40af;
    }
    .eq-orange {
      background: #fffbeb;
      border-left: 4px solid #d97706;
      color: #92400e;
    }
    .badge {
      font-size: 11px;
      font-weight: 700;
      padding: 2px 6px;
      border-radius: 4px;
      display: inline-flex;
      align-items: center;
      gap: 2px;
    }
    .badge-true {
      background: #dcfce7;
      color: #15803d;
    }
    .badge-false {
      background: #fee2e2;
      color: #b91c1c;
    }
    .verdict-box {
      margin-top: 4px;
      padding: 8px;
      border-radius: 8px;
      text-align: center;
      font-weight: 700;
      font-size: 13px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: all 0.2s ease;
    }
    .verdict-no {
      background: #fef2f2;
      color: #dc2626;
      border: 1px solid #fecaca;
    }
    .verdict-yes {
      background: #f0fdf4;
      color: #16a34a;
      border: 1px solid #bbf7d0;
    }
    .pt-marker {
      transition: transform 0.2s ease, opacity 0.2s ease;
      cursor: pointer;
    }
  </style>
</head>
<body>

  <div class="tabs">
    <button class="tab-btn active" id="tab0" onclick="selectPoint(0)">(3, 5)</button>
    <button class="tab-btn" id="tab1" onclick="selectPoint(1)">(0, 5)</button>
    <button class="tab-btn" id="tab2" onclick="selectPoint(2)">(2, 3) ★</button>
  </div>

  <div class="layout">
    <div class="graph-container">
      <svg viewBox="0 0 280 260">
        
        <g stroke="#e2e8f0" stroke-width="1">
          <line x1="35" y1="212" x2="263" y2="212" />
          <line x1="35" y1="179" x2="263" y2="179" />
          <line x1="35" y1="146" x2="263" y2="146" />
          <line x1="35" y1="113" x2="263" y2="113" />
          <line x1="35" y1="80" x2="263" y2="80" />
          <line x1="35" y1="47" x2="263" y2="47" />

          <line x1="73" y1="35" x2="73" y2="245" />
          <line x1="111" y1="35" x2="111" y2="245" />
          <line x1="149" y1="35" x2="149" y2="245" />
          <line x1="187" y1="35" x2="187" y2="245" />
          <line x1="225" y1="35" x2="225" y2="245" />
        </g>

        
        <g stroke="#94a3b8" stroke-width="1.5">
          <line x1="35" y1="245" x2="265" y2="245" />
          <line x1="35" y1="245" x2="35" y2="25" />
        </g>

        
        <g font-size="10" fill="#64748b" text-anchor="middle" font-weight="600">
          <text x="35" y="258">0</text>
          <text x="73" y="258">1</text>
          <text x="111" y="258">2</text>
          <text x="149" y="258">3</text>
          <text x="187" y="258">4</text>
          <text x="225" y="258">5</text>
          <text x="260" y="258">x</text>

          <text x="24" y="215">1</text>
          <text x="24" y="182">2</text>
          <text x="24" y="149">3</text>
          <text x="24" y="116">4</text>
          <text x="24" y="83">5</text>
          <text x="24" y="50">6</text>
          <text x="24" y="28">y</text>
        </g>

        
        <line x1="54" y1="245" x2="168" y2="47" stroke="#2563eb" stroke-width="2.5" stroke-linecap="round" />
        <text x="172" y="44" fill="#2563eb" font-size="10" font-weight="700">y = 2x - 1</text>

        
        <line x1="20" y1="67" x2="235" y2="252" stroke="#d97706" stroke-width="2.5" stroke-linecap="round" />
        <text x="200" y="235" fill="#d97706" font-size="10" font-weight="700">y = -x + 5</text>

        
        <g class="pt-marker" id="marker0" onclick="selectPoint(0)">
          <circle id="halo0" cx="149" cy="80" r="10" fill="none" stroke="#2563eb" stroke-width="2" opacity="1" />
          <circle cx="149" cy="80" r="5" fill="#2563eb" />
          <text x="156" y="76" font-size="10" font-weight="700" fill="#1e2945">(3,5)</text>
        </g>

        
        <g class="pt-marker" id="marker1" onclick="selectPoint(1)">
          <circle id="halo1" cx="35" cy="80" r="10" fill="none" stroke="#d97706" stroke-width="2" opacity="0" />
          <circle cx="35" cy="80" r="5" fill="#d97706" />
          <text x="42" y="74" font-size="10" font-weight="700" fill="#1e2945">(0,5)</text>
        </g>

        
        <g class="pt-marker" id="marker2" onclick="selectPoint(2)">
          <circle id="halo2" cx="111" cy="146" r="10" fill="none" stroke="#16a34a" stroke-width="2" opacity="0" />
          <circle cx="111" cy="146" r="6" fill="#16a34a" />
          <text x="119" y="142" font-size="10" font-weight="700" fill="#16a34a">(2,3)</text>
        </g>
      </svg>
    </div>

    <div class="eval-card">
      <div style="font-size: 12px; font-weight: 700; color: #64748b;" id="pointHeader">TESTING POINT (3, 5)</div>

      <div class="eq-row eq-blue">
        <div>
          <span>y = 2x - 1</span><br>
          <span style="font-size: 11px; font-weight: normal; opacity: 0.9;" id="sub1">5 = 2(3) - 1</span>
        </div>
        <div class="badge badge-true" id="badge1">✓ TRUE</div>
      </div>

      <div class="eq-row eq-orange">
        <div>
          <span>y = -x + 5</span><br>
          <span style="font-size: 11px; font-weight: normal; opacity: 0.9;" id="sub2">5 = -(3) + 5</span>
        </div>
        <div class="badge badge-false" id="badge2">✗ FALSE</div>
      </div>

      <div class="verdict-box verdict-no" id="verdict">
        <span id="verdictIcon">✗</span>
        <span id="verdictText">Not a Solution</span>
      </div>
    </div>
  </div>

  <script>
    const data = [
      {
        header: 'TESTING POINT (3, 5)',
        sub1: '5 = 2(3) - 1  →  5 = 5',
        b1True: true,
        sub2: '5 = -(3) + 5  →  5 ≠ 2',
        b2True: false,
        valid: false,
        verdict: 'Not a Solution (Line 1 only)'
      },
      {
        header: 'TESTING POINT (0, 5)',
        sub1: '5 = 2(0) - 1  →  5 ≠ -1',
        b1True: false,
        sub2: '5 = -(0) + 5  →  5 = 5',
        b2True: true,
        valid: false,
        verdict: 'Not a Solution (Line 2 only)'
      },
      {
        header: 'TESTING POINT (2, 3)',
        sub1: '3 = 2(2) - 1  →  3 = 3',
        b1True: true,
        sub2: '3 = -(2) + 5  →  3 = 3',
        b2True: true,
        valid: true,
        verdict: 'System Solution!'
      }
    ];

    function selectPoint(idx) {
      // Update tabs
      for (let i = 0; i < 3; i++) {
        document.getElementById('tab' + i).classList.toggle('active', i === idx);
        document.getElementById('halo' + i).setAttribute('opacity', i === idx ? '1' : '0');
      }

      const d = data[idx];
      document.getElementById('pointHeader').textContent = d.header;
      document.getElementById('sub1').textContent = d.sub1;
      document.getElementById('sub2').textContent = d.sub2;

      // Badge 1
      const b1 = document.getElementById('badge1');
      b1.className = 'badge ' + (d.b1True ? 'badge-true' : 'badge-false');
      b1.textContent = d.b1True ? '✓ TRUE' : '✗ FALSE';

      // Badge 2
      const b2 = document.getElementById('badge2');
      b2.className = 'badge ' + (d.b2True ? 'badge-true' : 'badge-false');
      b2.textContent = d.b2True ? '✓ TRUE' : '✗ FALSE';

      // Verdict
      const v = document.getElementById('verdict');
      v.className = 'verdict-box ' + (d.valid ? 'verdict-yes' : 'verdict-no');
      document.getElementById('verdictIcon').textContent = d.valid ? '✓' : '✗';
      document.getElementById('verdictText').textContent = d.verdict;
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 12px 8px;
      display: flex;
      justify-content: center;
      align-items: center;
      min-height: 100%;
    }

    .main-layout {
      display: flex;
      flex-direction: row;
      flex-wrap: wrap;
      gap: 16px;
      justify-content: center;
      align-items: center;
      max-width: 650px;
      width: 100%;
    }

    .graph-container {
      position: relative;
      width: 290px;
      height: 290px;
      flex-shrink: 0;
      user-select: none;
    }

    svg {
      width: 100%;
      height: 100%;
      display: block;
      overflow: visible;
    }

    .tables-container {
      display: flex;
      gap: 12px;
      flex-wrap: wrap;
      justify-content: center;
      align-items: flex-start;
    }

    .table-card {
      background: #ffffff;
      border-radius: 8px;
      border: 1.5px solid #e2e8f0;
      padding: 6px 10px;
      width: 124px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
    }

    .table-title {
      font-size: 13px;
      font-weight: 700;
      text-align: center;
      padding: 4px 0 6px;
      border-bottom: 1.5px solid #f1f5f9;
    }

    .t-blue { color: #0284c7; }
    .t-orange { color: #ea580c; }

    table {
      width: 100%;
      border-collapse: collapse;
      margin-top: 4px;
      font-size: 13px;
      text-align: center;
    }

    th {
      font-weight: 600;
      color: #64748b;
      padding: 3px 0;
      font-size: 12px;
    }

    td {
      padding: 3px 0;
      color: #334155;
      font-variant-numeric: tabular-nums;
    }

    tr.shared-row {
      background: #dcfce7;
      border-radius: 4px;
    }

    tr.shared-row td {
      color: #15803d;
      font-weight: 700;
    }

    .callout-badge {
      font-size: 10px;
      font-weight: 700;
      fill: #15803d;
    }

    @media (max-width: 360px) {
      .graph-container {
        width: 270px;
        height: 270px;
      }
      .table-card {
        width: 115px;
      }
    }
  </style>
</head>
<body>

<div class="main-layout">
  
  <div class="graph-container">
    <svg viewBox="0 0 300 300">
      <defs>
        
        <marker id="arrow" viewBox="0 0 6 6" refX="3" refY="3" markerWidth="4" markerHeight="4" orient="auto-start-reverse">
          <path d="M 0 1.5 L 4.5 3 L 0 4.5 z" fill="#94a3b8"/>
        </marker>
        <filter id="shadow" x="-10%" y="-10%" width="130%" height="130%">
          <feDropShadow dx="0" dy="1" stdDeviation="1.5" flood-opacity="0.12"/>
        </filter>
      </defs>

      
      
      <g stroke="#f1f5f9" stroke-width="1.5">
        
        <line x1="30" y1="30" x2="30" y2="270" />
        <line x1="60" y1="30" x2="60" y2="270" />
        <line x1="120" y1="30" x2="120" y2="270" />
        <line x1="150" y1="30" x2="150" y2="270" />
        <line x1="180" y1="30" x2="180" y2="270" />
        <line x1="210" y1="30" x2="210" y2="270" />
        <line x1="240" y1="30" x2="240" y2="270" />
        <line x1="270" y1="30" x2="270" y2="270" />
        
        
        <line x1="30" y1="30" x2="270" y2="30" />
        <line x1="30" y1="60" x2="270" y2="60" />
        <line x1="30" y1="90" x2="270" y2="90" />
        <line x1="30" y1="120" x2="270" y2="120" />
        <line x1="30" y1="150" x2="270" y2="150" />
        <line x1="30" y1="180" x2="270" y2="180" />
        <line x1="30" y1="240" x2="270" y2="240" />
        <line x1="30" y1="270" x2="270" y2="270" />
      </g>

      
      <g stroke="#94a3b8" stroke-width="1.75">
        
        <line x1="20" y1="210" x2="285" y2="210" marker-end="url(#arrow)" />
        
        <line x1="90" y1="280" x2="90" y2="15" marker-end="url(#arrow)" />
      </g>

      
      <g font-size="10" fill="#94a3b8" text-anchor="middle" font-weight="600">
        
        <text x="30" y="224">-2</text>
        <text x="150" y="224">2</text>
        <text x="210" y="224">4</text>
        <text x="270" y="224">6</text>
        <text x="288" y="206" fill="#64748b" font-weight="700">x</text>

        
        <text x="78" y="273">-2</text>
        <text x="78" y="153">2</text>
        <text x="78" y="93">4</text>
        <text x="78" y="33">6</text>
        <text x="90" y="10" fill="#64748b" font-weight="700">y</text>
      </g>

      
      
      <line x1="67.5" y1="285" x2="202.5" y2="15" stroke="#0284c7" stroke-width="2.5" stroke-linecap="round" />
      
      
      
      <line x1="45" y1="15" x2="285" y2="255" stroke="#ea580c" stroke-width="2.5" stroke-linecap="round" />

      
      <circle cx="90" cy="240" r="3.5" fill="#0284c7" />
      <circle cx="120" cy="180" r="3.5" fill="#0284c7" />
      <circle cx="180" cy="60" r="3.5" fill="#0284c7" />

      
      <circle cx="90" cy="60" r="3.5" fill="#ea580c" />
      <circle cx="210" cy="180" r="3.5" fill="#ea580c" />
      <circle cx="240" cy="210" r="3.5" fill="#ea580c" />

      
      <g font-size="11" font-weight="700">
        <text x="206" y="28" fill="#0284c7">y = 2x − 1</text>
        <text x="214" y="166" fill="#ea580c">y = −x + 5</text>
      </g>

      
      <g>
        
        <circle cx="150" cy="120" r="6" fill="none" stroke="#eab308" stroke-width="2.5">
          <animate attributeName="r" values="6; 13; 19" dur="2.4s" repeatCount="indefinite" keyTimes="0; 0.5; 1" />
          <animate attributeName="stroke-opacity" values="0.9; 0.45; 0" dur="2.4s" repeatCount="indefinite" keyTimes="0; 0.5; 1" />
        </circle>
        
        
        <circle cx="150" cy="120" r="5" fill="#15803d" stroke="#ffffff" stroke-width="2" />
        
        
        <g filter="url(#shadow)">
          <rect x="36" y="93" width="108" height="20" rx="4" fill="#ffffff" stroke="#15803d" stroke-width="1.2" />
          <text x="90" y="107" class="callout-badge" text-anchor="middle">Intersection (2, 3)</text>
          <line x1="144" y1="103" x2="147" y2="116" stroke="#15803d" stroke-width="1.2" />
        </g>
      </g>
    </svg>
  </div>

  
  <div class="tables-container">
    
    <div class="table-card">
      <div class="table-title t-blue">y = 2x − 1</div>
      <table>
        <thead>
          <tr><th>x</th><th>y</th></tr>
        </thead>
        <tbody>
          <tr><td>0</td><td>-1</td></tr>
          <tr><td>1</td><td>1</td></tr>
          <tr class="shared-row"><td>2</td><td>3</td></tr>
          <tr><td>3</td><td>5</td></tr>
        </tbody>
      </table>
    </div>

    
    <div class="table-card">
      <div class="table-title t-orange">y = −x + 5</div>
      <table>
        <thead>
          <tr><th>x</th><th>y</th></tr>
        </thead>
        <tbody>
          <tr><td>0</td><td>5</td></tr>
          <tr class="shared-row"><td>2</td><td>3</td></tr>
          <tr><td>4</td><td>1</td></tr>
          <tr><td>5</td><td>0</td></tr>
        </tbody>
      </table>
    </div>
  </div>
</div>

</body>
</html>

Solving Multi-Step Linear Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides and Rational Coefficients

Solving Linear Equations with Fractional Coefficients

Clearing Decimals in Multi-Step Linear Equations

Solving Equations with Distributive Property on Both Sides

Identifying Equations with One Solution, No Solution, or Infinite Solutions

OGM.8.ALG.4

Aligned learning resources

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