# Lesson 7

Inequivalent Equations

### Lesson Narrative

In this lesson, students continue to investigate solutions to equations that involve squares and square roots. In particular, they find that squaring each side of an equation may result in a new equation that has solutions that are not solutions to the original equation. They also recall that taking the square root of each side of an equation runs the risk of ignoring some solutions, as first discussed in a previous course. The key idea is to think carefully about solutions when using squares or square roots to solve an equation.

Students reason abstractly and quantitatively when they analyze possible solutions to equations involving squares and square roots (MP2).

### Learning Goals

Teacher Facing

• Explain why squaring each side of an equation, or taking the square root of each side, may result in an inequivalent equation.
• Use graphs to represent solutions to equations involving squares and square roots.

### Student Facing

• Let’s see what happens when we square each side of an equation.

### Student Facing

• I can solve equations by squaring or finding square roots.