In this lesson, students learn that equivalent equations are equations with the exact same solutions. Students see that the moves that generate equivalent expressions (for example, applying the distributive property or combining like terms) can also create equivalent equations. Additionally, an equivalent equation can be created by adding the same value to each side or multiplying each side by the same non-zero number. Students have seen moves like this before, when solving one-variable equations in middle school. What is new here is an awareness that each of the equations created as a part of the solving process is equivalent to the original equation.

Students also regard equivalent equations as synonymous statements about a relationship. They use context to interpret the solution to equivalent equations, and to think about why it makes sense that equivalent equations have the same solution. In doing so, students reason abstractly and quantitatively (MP2).