Eighth Grade · Math · week 1

Multi-step equations

Solve multi-step linear equations in one variable using the distributive property and combining like terms.

Some equations take more than one move to solve. Before you can undo anything, you often need to distribute (multiply through a parenthesis) or combine like terms on each side, so that each side is a simple expression. Only after that simplifying step do you start doing the same thing to both sides to isolate x.

A good habit: look for parentheses first (distribute them away) and any like terms sitting on the same side (combine them), and only then start moving terms across the equals sign. Finish every problem by substituting your answer back into the ORIGINAL equation to check it -- that ten-second habit catches almost every mistake.

📋 For the teacher
Teach it (10–15 min):
  • Say out loud: "parentheses and like terms first, THEN move things across the equals sign." That order avoids most mistakes.
  • Combine like terms on each side separately before doing anything to both sides -- a side is not ready to work with until it is fully simplified.
  • Teach the check habit from week one: substitute the answer back into the ORIGINAL equation. It takes ten seconds and it is the best error-catcher there is.
  • Point out that 3(2x - 1) = 33 can be solved two legal ways (distribute first, or divide both sides by 3 first) -- let them pick, and notice both give the same answer.
Talk about it:
  • Why do we combine like terms or distribute before moving anything across the equals sign?
  • When solving 3(2x - 1) = 33, is it faster to distribute or to divide both sides by 3 first? Why?
  • How can you check that x = 7 really solves 2(x + 5) = 24?

Mastery looks like: They can solve a two- or three-step equation involving distribution and/or combining like terms, and check the result by substitution.

Common stumbles: Forgetting to distribute to BOTH terms inside a parenthesis; combining terms from different sides of the equation as if they were on the same side.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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