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.
- 1Distribute to remove parentheses.
- 2Combine like terms on each side.
- 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.
Solve 2(x + 3) + 4 = 18.
- 1Distribute: 2x + 6 + 4 = 18.
- 2Combine: 2x + 10 = 18.
- 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
- A repeatable plan
- Distribute to remove parentheses.
- Combine like terms on each side.
- Undo addition or subtraction, then multiplication or division.
Video walkthrough
Solving 2-Step Equations
Undo operations in reverse - the same idea extends to multi-step equations.
Watch on YouTubePractice
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 yourselfSolve: x + 9 = 15.
Step-by-step solution
- 1Subtract 9 from both sides: x = 15 − 9.
- 2x = 6.
- 3Check: 6 + 9 = 15 ✓.
Exercise 2
Try it yourselfSolve: 4x = 28.
Step-by-step solution
- 1Divide both sides by 4: x = 28 ÷ 4.
- 2x = 7.
- 3Check: 4(7) = 28 ✓.
Exercise 3
Try it yourselfSolve: 2(x − 5) = 14.
Step-by-step solution
- 1Divide both sides by 2: x − 5 = 7.
- 2Add 5: x = 12.
- 3Check: 2(12 − 5) = 2(7) = 14 ✓.
Exercise 4
Try it yourselfSolve: 3x + 2x − 7 = 18.
Step-by-step solution
- 1Combine 3x + 2x = 5x: 5x − 7 = 18.
- 2Add 7: 5x = 25.
- 3Divide by 5: x = 5.
Exercise 5
Try it yourselfSolve: 2(3x + 1) − 4 = 20.
Step-by-step solution
- 1Distribute: 6x + 2 − 4 = 20 → 6x − 2 = 20.
- 2Add 2: 6x = 22.
- 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
Solve: 3(x - 2) = 12.