Unit 2 · Topic 1

Multi-Step Equations

Overview

Combine like terms and use inverse operations to solve.

Topic 1 of 2~54 min
Unit overview

The lesson

This lesson teaches Multi-Step Equations. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

A repeatable plan

When you study a repeatable plan, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

  1. 1Distribute to remove parentheses.
  2. 2Combine like terms on each side.
  3. 3Undo addition or subtraction, then multiplication or division.

An equation says two expressions have the same value. Whatever you do to one side, you must do to the other to keep the balance.

Check your solution by substituting it back into the original equation. If both sides match, your answer is correct.

Worked example

Solve 2(x + 3) + 4 = 18.

  1. 1Distribute: 2x + 6 + 4 = 18.
  2. 2Combine: 2x + 10 = 18.
  3. 3Subtract 10: 2x = 8. Divide by 2: x = 4.

Why this matters

Multi-Step Equations shows up constantly in combine like terms and use inverse operations to solve. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

  1. A repeatable plan
  2. Distribute to remove parentheses.
  3. Combine like terms on each side.
  4. Undo addition or subtraction, then multiplication or division.

Video walkthrough

Math Antics

Solving 2-Step Equations

Undo operations in reverse - the same idea extends to multi-step equations.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

Solve: x + 9 = 15.

Step-by-step solution

  1. 1Subtract 9 from both sides: x = 15 − 9.
  2. 2x = 6.
  3. 3Check: 6 + 9 = 15 ✓.

Exercise 2

Try it yourself

Solve: 4x = 28.

Step-by-step solution

  1. 1Divide both sides by 4: x = 28 ÷ 4.
  2. 2x = 7.
  3. 3Check: 4(7) = 28 ✓.

Exercise 3

Try it yourself

Solve: 2(x − 5) = 14.

Step-by-step solution

  1. 1Divide both sides by 2: x − 5 = 7.
  2. 2Add 5: x = 12.
  3. 3Check: 2(12 − 5) = 2(7) = 14 ✓.

Exercise 4

Try it yourself

Solve: 3x + 2x − 7 = 18.

Step-by-step solution

  1. 1Combine 3x + 2x = 5x: 5x − 7 = 18.
  2. 2Add 7: 5x = 25.
  3. 3Divide by 5: x = 5.

Exercise 5

Try it yourself

Solve: 2(3x + 1) − 4 = 20.

Step-by-step solution

  1. 1Distribute: 6x + 2 − 4 = 20 → 6x − 2 = 20.
  2. 2Add 2: 6x = 22.
  3. 3Divide by 6: x = 11/3.

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Multi-Step Equations

Question 1 of 4

Easy

Solve: 3(x - 2) = 12.

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