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      background: #fef3c7;
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      justify-content: center;
      gap: 8px;
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      color: #1d4ed8;
      border: 1px dashed #2563eb;
    }
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</head>
<body>

  <div class="columns">
    
    <div class="col-panel panel-orange">
      <div class="panel-header">
        <span class="panel-title" style="color: #b45309;">
          Single-Side Properties
        </span>
        <span class="badge-orange">1 Side</span>
      </div>

      
      <div class="math-card">
        <span class="card-label">Distributive</span>
        <div class="card-content">
          <span>3(x + 2)</span>
          <span class="arrow">→</span>
          <span class="hl-orange">3x + 6</span>
        </div>
      </div>

      
      <div class="math-card">
        <span class="card-label">Combining Like Terms</span>
        <div class="card-content">
          <span>3x + 2x</span>
          <span class="arrow">→</span>
          <span class="hl-orange">5x</span>
        </div>
      </div>

      <div class="balance-vis">
        <span class="side-tag side-tag-orange">Rewrites Expression Only</span>
      </div>
    </div>

    
    <div class="col-panel panel-blue">
      <div class="panel-header">
        <span class="panel-title" style="color: #1d4ed8;">
          Properties of Equality
        </span>
        <span class="badge-blue">Both Sides</span>
      </div>

      
      <div class="math-card">
        <span class="card-label">Addition Property of Equality</span>
        <div class="balance-box">
          <div class="balance-eq">
            5x − 4 = 16
          </div>
          <span class="arrow">↓</span>
          <div class="balance-eq">
            5x − 4 <span class="hl-blue">+ 4</span> = 16 <span class="hl-blue">+ 4</span>
          </div>
        </div>
      </div>

      <div class="balance-vis">
        <span class="side-tag side-tag-blue">⚖️ Maintains Equal Balance</span>
      </div>
    </div>
  </div>

</body>
</html>

Justifying Steps in Solving Linear Equations Using Properties of Equality

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  <title>Two-Column Algebraic Proof</title>
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    .math var {
      font-style: italic;
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      transition: background 0.2s ease, transform 0.2s ease;
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        padding: 0 4px;
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        padding: 6px 8px;
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  </style>
</head>
<body>

  <div class="proof-wrapper">
    
    <div class="controls-bar">
      <div class="step-indicator" id="stepCounter">Step 1 of 6</div>
      <div class="btn-group">
        <button class="ctrl-btn" id="prevBtn" title="Previous Step">◀</button>
        <button class="ctrl-btn" id="playBtn" title="Auto Play">▶ Play</button>
        <button class="ctrl-btn" id="nextBtn" title="Next Step">▶</button>
      </div>
    </div>

    
    <table class="proof-table" role="grid" aria-label="Algebraic Proof Table">
      <thead class="table-header">
        <tr>
          <th scope="col">Statement</th>
          <th scope="col">Reason / Justification</th>
        </tr>
      </thead>
      <tbody id="proofBody">
        <tr class="proof-row active" data-step="0">
          <td>
            <span class="row-num">1.</span>
            <span class="math">4(<var>x</var> − 2) + 7 = 2<var>x</var> + 13</span>
          </td>
          <td>
            <div class="reason-title">Given</div>
          </td>
        </tr>

        <tr class="proof-row" data-step="1">
          <td>
            <span class="row-num">2.</span>
            <span class="math">4<var>x</var> − 8 + 7 = 2<var>x</var> + 13</span>
          </td>
          <td>
            <div class="reason-title">Distributive Property</div>
          </td>
        </tr>

        <tr class="proof-row" data-step="2">
          <td>
            <span class="row-num">3.</span>
            <span class="math">4<var>x</var> − 1 = 2<var>x</var> + 13</span>
          </td>
          <td>
            <div class="reason-title">Simplify</div>
            <span class="reason-action">Combine like terms</span>
          </td>
        </tr>

        <tr class="proof-row" data-step="3">
          <td>
            <span class="row-num">4.</span>
            <span class="math">2<var>x</var> − 1 = 13</span>
          </td>
          <td>
            <div class="reason-title">Subtraction Property of Equality</div>
            <span class="reason-action">− 2<var>x</var> both sides</span>
          </td>
        </tr>

        <tr class="proof-row" data-step="4">
          <td>
            <span class="row-num">5.</span>
            <span class="math">2<var>x</var> = 14</span>
          </td>
          <td>
            <div class="reason-title">Addition Property of Equality</div>
            <span class="reason-action">+ 1 both sides</span>
          </td>
        </tr>

        <tr class="proof-row" data-step="5">
          <td>
            <span class="row-num">6.</span>
            <span class="math"><var>x</var> = 7</span>
          </td>
          <td>
            <div class="reason-title">Division Property of Equality</div>
            <span class="reason-action">÷ 2 both sides</span>
          </td>
        </tr>
      </tbody>
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      <div class="dot" data-step="3" title="Step 4"></div>
      <div class="dot" data-step="4" title="Step 5"></div>
      <div class="dot" data-step="5" title="Step 6"></div>
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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Multiplication Property of Equality Comparison</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      width: 100%;
      background: #f8f9fa;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      padding: 14px;
      display: flex;
      flex-direction: column;
      justify-content: center;
      min-height: 100vh;
    }
    .grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 14px;
      width: 100%;
      max-width: 660px;
      margin: 0 auto;
    }
    @media (max-width: 520px) {
      .grid {
        grid-template-columns: 1fr;
        gap: 12px;
      }
      body {
        padding: 8px;
        min-height: auto;
      }
    }
    .column {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 14px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
      position: relative;
      box-shadow: 0 1px 3px rgba(0,0,0,0.03);
    }
    .column.bad {
      border-top: 4px solid #ef4444;
    }
    .column.good {
      border-top: 4px solid #10b981;
    }
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      display: flex;
      flex-direction: column;
      align-items: center;
      text-align: center;
      gap: 2px;
    }
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      display: flex;
      align-items: center;
      gap: 5px;
      font-size: 13px;
      font-weight: 800;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }
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      font-size: 12px;
      font-weight: 600;
      color: #64748b;
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      justify-content: center;
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</head>
<body>

  <div class="grid">
    
    <div class="column bad">
      <div class="header">
        <div class="header-tag">
          <span>✕</span>
          <span>Incorrect</span>
        </div>
        <div class="header-sub">Selective Term Multiplication</div>
      </div>

      <div class="step-box">
        
        <div class="math-row">
          <span class="frac"><span class="num"><span class="var">x</span></span><span class="den">2</span></span>
          <span class="op">+</span>
          <span>5</span>
          <span class="op">=</span>
          <span>9</span>
        </div>

        <div class="arrow">↓</div>

        
        <div class="math-row">
          <span class="red-text">2 · </span>
          <span class="frac"><span class="num"><span class="var">x</span></span><span class="den">2</span></span>
          <span class="op">+</span>
          <span>5</span>
          <span class="op">=</span>
          <span class="red-text">2 · </span>
          <span>9</span>
        </div>

        <div class="arrow">↓</div>

        
        <div class="math-row">
          <span class="var">x</span>
          <span class="op">+</span>
          <span class="bad-highlight">5</span>
          <span class="op">=</span>
          <span>18</span>
        </div>
      </div>

      <div class="tag bad">⚠️ Forgot to multiply the +5!</div>
    </div>

    
    <div class="column good">
      <div class="header">
        <div class="header-tag">
          <span>✓</span>
          <span>Correct</span>
        </div>
        <div class="header-sub">Entire Expression Multiplied</div>
      </div>

      <div class="step-box">
        
        <div class="math-row">
          <span class="frac"><span class="num"><span class="var">x</span></span><span class="den">2</span></span>
          <span class="op">+</span>
          <span>5</span>
          <span class="op">=</span>
          <span>9</span>
        </div>

        <div class="arrow">↓</div>

        
        <div class="math-row">
          <span class="green-text">2 · </span>
          <span class="paren-lg">(</span>
          <span class="frac"><span class="num"><span class="var">x</span></span><span class="den">2</span></span>
          <span class="op">+</span>
          <span>5</span>
          <span class="paren-lg">)</span>
          <span class="op">=</span>
          <span class="green-text">2 · </span>
          <span class="paren">(</span><span>9</span><span class="paren">)</span>
        </div>

        <div class="arrow">↓</div>

        
        <div class="math-row">
          <span class="var">x</span>
          <span class="op">+</span>
          <span class="good-highlight">10</span>
          <span class="op">=</span>
          <span>18</span>
        </div>
      </div>

      <div class="tag good">✓ Multiplied all terms by 2</div>
    </div>
  </div>

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Solving Multi-Step Linear Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides and Rational Coefficients

Identifying Identities, Contradictions, and Conditional Linear Equations

Solving Linear Equations with Coefficients Represented by Letters

Rearranging Geometric Formulas and Multi-Variable Literal Equations

Rearranging Scientific and Physics Formulas for Specified Variables

Solving Multi-Step Linear Inequalities in One Variable

Solving Compound Inequalities with And and Or Conditions

Graphing Solutions to Linear Inequalities on a Number Line

Modeling and Solving Real-World Equations with Variables on Both Sides

math

Linear Equations, Literal Formulas, and Single-Variable Inequalities

Writing Linear Equations from Word Problems

Writing Quadratic Equations from Word Problems

Writing Simple Rational Equations from Word Problems

Writing Exponential Equations from Word Problems

Writing Inequalities from Word Problems

Writing Equations from Word Problems

Modeling with Linear Equations: Distance, Rate, and Time

Modeling with Linear Equations: Cost and Revenue

Modeling Area Problems with Quadratic Equations

Modeling Projectile Motion with Quadratic Equations

Modeling Exponential Growth

Modeling Exponential Decay

Choosing the Right Model for a Word Problem

Creating Equations from Geometric Word Problems

Writing and Solving Equations from Real-World Scenarios

Modeling Real-World Scenarios with Equations

Solving Literal Equations in One Step

Solving Literal Equations in Multiple Steps

Solving Literal Equations with Fractional Coefficients

Solving Literal Equations with Parentheses

Rearranging Mathematical Formulas

Rearranging Science Formulas

Literal Equations in Word Problems

Literal Equations and Formulas: Comprehensive Review

Literal Equations and Formulas

Solving Equations With Addition and Subtraction

Solving Equations With Multiplication and Division

Isolating a Variable in a Formula: One Step

Isolating a Variable in a Formula: Two Steps

Isolating a Variable in a Formula: Multi-Step

Rearranging Geometric Formulas

Rearranging Physics Formulas

Rearranging Formulas with Parentheses

Rearranging Formulas to Highlight a Quantity

方程的定义、方程的解与从算术到代数的思维转换

等式的基本性质及其在方程变形中的应用

合并同类项与移项解一元一次方程

去括号与去分母解复杂一元一次方程

列一元一次方程：行程问题与工程问题

列一元一次方程：进销利润与最佳方案决策

一元一次方程的解法与实际问题建模

Solving Equations With Inverse Operations

Explaining Each Step Using Properties of Equality

Justifying Steps with the Distributive Property

Justifying Steps with the Commutative and Associative Properties

Justifying Steps with the Inverse Properties

Constructing Viable Arguments for Solution Methods

Identifying Errors in Solution Steps

Justifying Steps with Combining Like Terms

Justifying Steps in Solving Equations

Solving Literal Equations with Multiple Steps

Solving Literal Equations with Grouping Symbols

Rearranging Scientific Formulas

Rearranging Geometry Formulas for a Variable

Solving Formulas with Squared Variables

Solving Formulas with Square Root Terms

Solving Formulas with Rational Expressions

Solving and Rearranging Literal Equations

二元一次方程（组）的概念与公共解的意义

代入消元法解二元一次方程组

加减消元法解二元一次方程组

三元一次方程组的消元解法

列二元一次方程组解决实际问题与解的合理性检验

二元与三元一次方程组及消元解法

The Mathematical Modeling Process

Modeling Real-World Situations with Equations

Communicating Mathematical Ideas with Multiple Representations

Using Precise Mathematical Language in Problem Solving

Comprehensive Modeling and Literal Equations Review

Mathematical Modeling and Communication

Solving Two-Step Linear Equations

Solving Linear Equations with the Distributive Property

Solving Linear Equations with Fractions

Solving Linear Equations with Decimals

Solving Linear Equations in One Variable

分式方程的定义与去分母转化为整式方程的思想

分式方程的增根成因与代入最简公分母验根法则

可化为一元一次方程的分式方程规范求解步骤

列分式方程解决工程、行程等实际应用问题

分式方程的解法与增根检验

Solving One-Step Linear Inequalities

Solving Two-Step Linear Inequalities

Solving Multi-Step Linear Inequalities

Solving Compound Inequalities: And

Solving Compound Inequalities: Or

Solving Linear Inequalities

一元二次方程的概念、一般形式 ax^2+bx+c=0 与各项系数

直接开平方法与配方法解一元二次方程

求根公式的推导与公式法解一元二次方程

因式分解法解一元二次方程

一元二次方程根的判别式 Δ 与根的情况判定

一元二次方程的根与系数的关系（韦达定理）及其代数求值

列一元二次方程：平均变化率与几何图形面积问题

一元二次方程的解法、判别式与根系关系

Solutions of a Linear Equation: Finding Pairs of Values

Identifying Equations with No Solution or Infinitely Many Solutions

Properties and Special Cases of Linear Equations

不等式的概念与现实不等关系的符号表征

不等式的基本性质与乘除负数时的不等号变向法则

解一元一次不等式并在数轴上表示解集

一元一次不等式组的解法与借助数轴确定公共解集

列一元一次不等式（组）解决实际方案选择与资源配置问题

一元一次不等式与不等式组

Reviewing One-Step and Two-Step Equations

Combining Like Terms to Solve Equations

Solving Equations with Parentheses and Grouping Symbols

Solving Equations with Variables on Both Sides

Solving Equations with Distribution and Variables on Both Sides

Solving Multi-Step Linear Equations

Identifying Equations with No Solution

Identifying Equations with Infinitely Many Solutions

Classifying Equations by Number of Solutions

Checking Solutions: Verifying Algebraically and Graphically

Analyzing Solutions and Justifying Steps in Linear Equations

Using Equations to Model Real-World Situations

Multi-Step Equation Word Problems

Linear Equation Fluency: Mixed Practice

Modeling and Applying Linear Equations

Introduction to Solving Linear Inequalities

Solving One-Step Inequalities with Addition and Subtraction

Solving One-Step Inequalities with Multiplication and Division

Solving and Graphing Linear Inequalities

Solving Inequalities with the Distributive Property

Solving Inequalities with Variables on Both Sides

Inequalities with No Solution or All Real Numbers

Solving Compound Inequalities (AND)

Solving Compound Inequalities (OR)

Linear Inequalities in Real-World Applications

Linear Inequality Word Problems

Linear Inequality Fluency: Mixed Practice

Advanced Linear Inequalities and Applications

Solving Equations with Fractional Coefficients and Variables on Both Sides

Identifying No Solution and Infinite Solutions in Linear Equations

Solving Literal Equations for a Specific Variable

Solving Linear Inequalities with the Distributive Property

Solving Linear Inequalities with Variables on Both Sides

Writing and Solving Multi-Step Inequalities from Word Problems

Solving Linear Equations and Inequalities

OGM.10.REI.1

OGM.10.REI.1

Aligned learning resources

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