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Two-Step Equations

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

Two-step equations usually have two operations attached to the variable. Undo addition or subtraction first, then undo multiplication or division. Each step must keep both sides balanced. In Algebra Readiness, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

Why it matters: Phone bills with a flat fee plus a per-minute rate, gym memberships with a startup cost, and rideshare totals all model with two-step equations. Two reverse moves unwind the total back to the unknown.

Worked example

Problem. Solve 3x + 5 = 20.

  1. Subtract 5 from both sides: 3x = 15.
  2. Divide both sides by 3.
  3. x = 5.
  4. Connect the calculation back to Two-Step Equations so the method, not just the arithmetic, is clear.

Answer: 5

Practice problems

1. Solve 2x + 3 = 11.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve 2x + 3 = 11.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract 3 from both sides: 2x = 8.
  4. Divide by 2 to get x = 4.
  5. Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.

Answer: 4

2. Solve 5x - 4 = 21.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve 5x - 4 = 21.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Add 4 to both sides: 5x = 25.
  4. Divide by 5 to get x = 5.
  5. Check the result by substituting or estimating: the response should match 5 and make sense in the original problem.

Answer: 5

3. Solve x/3 + 2 = 8.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve x/3 + 2 = 8.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract 2: x/3 = 6.
  4. Multiply by 3 to get x = 18.
  5. Check the result by substituting or estimating: the response should match 18 and make sense in the original problem.

Answer: 18

4. Solve 4n + 7 = 31.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Solve 4n + 7 = 31.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract 7: 4n = 24.
  4. Divide by 4: n = 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 6a - 9 = 15.

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

Answer: 4

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