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Multi-Step Equations

A free Algebra I lesson from the “Algebra Foundations” unit, with a worked example and practice problems including step-by-step solutions.

Multi-step equations may require simplifying both sides before isolating the variable. Keep equations balanced by doing the same operation to both sides.

What you'll learn

Why it matters: Budgeting, billing, and measurement problems often start with a total and ask you to undo several steps to find the missing amount.

Worked example

Problem. Solve 2x + 7 = 19.

  1. Subtract 7 from both sides: 2x = 12.
  2. Divide both sides by 2.
  3. x = 6.

Answer: 6

Practice problems

1. Solve 3x + 5 = 20.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve 3x + 5 = 20.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract 5 from both sides: 3x = 15.
  4. Divide by 3: x = 5.
  5. Check the result by substituting or estimating: the response should match 5 and make sense in the original problem.

Answer: 5

2. Solve 4x - 9 = 15.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve 4x - 9 = 15.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Add 9 to both sides: 4x = 24.
  4. Divide by 4: x = 6.
  5. Check the result by substituting or estimating: the response should match 6 and make sense in the original problem.

Answer: 6

3. What is the first step for 5x + 8 = 33?

Choices: Subtract 8 · Add 8 · Divide by 5 · Multiply by 5

Show solution
  1. Warm-up: First identify exactly what the question is asking: What is the first step for 5x + 8 = 33?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Undo the +8 before dividing.
  4. Subtract 8 from both sides.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Subtract 8

4. Solve 7x + 2 = 44.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Solve 7x + 2 = 44.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract 2: 7x = 42.
  4. Divide by 7: x = 6.
  5. Check the result by substituting or estimating: the response should match 6 and make sense in the original problem.

Answer: 6

5. Solve 9 - 2x = 21.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Solve 9 - 2x = 21.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract 9 from both sides: -2x = 12.
  4. Divide by -2: x = -6.
  5. Check the result by substituting or estimating: the response should match -6 and make sense in the original problem.

Answer: -6

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