AI Tutor
What happens when you solve an equation step-by-step, only for all your variables to vanish into thin air, leaving you with 5=55 = 5 or 0=70 = 7?
Your math didn't break—the equation is telling you exactly how many solutions exist across the entire real number line.
Let's look first at the classic case you solve most often: an equation that settles on a single value.

Conditional Equations

A conditional equation is an equation that is true on the condition that the variable takes on one specific value.
For example, in 4x−5=2x+74x - 5 = 2x + 7, subtracting 2x2x and adding 55 isolates the variable to reveal exactly one solution: x=6x = 6.
What happens if every variable term cancels out and leaves behind an undeniable mathematical truth?

Identity Equations

An identity is an equation that is always true for every real number you could ever plug into it.
When you expand 3(2x+4)=6x+123(2x + 4) = 6x + 12, both sides become identical: subtracting 6x6x yields 12=1212 = 12, meaning there are infinitely many solutions (all real numbers, denoted R\mathbb{R}).