The lesson
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
- 1Distribute to remove parentheses.
- 2Combine like terms on each side.
- 3Undo addition or subtraction, then multiplication or division.
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
Combine like terms and use inverse operations to solve.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Reversing the order named in the problem. Write the ratio in the same order the words give you.
Treating a part-to-part ratio like a part-to-whole fraction without checking what the whole is.
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 walkthroughs
Solving 2-Step Equations
Undo operations in reverse - the same idea extends to multi-step equations.
Watch on YouTube
Why We Do the Same Thing to Both Sides
Balance multi-step equations by keeping both sides equal.
Watch on YouTube
Multi-Step Equation Example
Clear fractions and solve a multi-step linear equation.
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 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.