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One-Step Equations

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

An equation is balanced when both sides are equal. To solve for a variable, undo the operation connected to it. Addition and subtraction undo each other; multiplication and division undo each other. 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: Working out the original price after a discount, the missing side of a recipe, or the unknown piece of a budget is one-step equation work. Undoing the operation is what isolates the variable.

Worked example

Problem. Solve x - 7 = 15.

  1. The variable has 7 subtracted from it.
  2. Undo subtraction by adding 7 to both sides.
  3. x = 22. Check: 22 - 7 = 15.
  4. Connect the calculation back to One-Step Equations so the method, not just the arithmetic, is clear.

Answer: 22

Practice problems

1. Solve x + 9 = 24.

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

Answer: 15

2. Solve y - 6 = 11.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve y - 6 = 11.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Add 6 to both sides.
  4. 11 + 6 = 17.
  5. Check the result by substituting or estimating: the response should match 17 and make sense in the original problem.

Answer: 17

3. Solve 4x = 28.

Choices: 7 · 24 · 32 · 112

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve 4x = 28.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Undo multiplication by dividing by 4.
  4. 28 divided by 4 equals 7.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 7

4. Solve n/5 = 6.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Solve n/5 = 6.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Undo division by multiplying both sides by 5.
  4. 6 x 5 = 30.
  5. Check the result by substituting or estimating: the response should match 30 and make sense in the original problem.

Answer: 30

5. Solve a - 13 = 8.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Solve a - 13 = 8.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Add 13 to both sides.
  4. 8 + 13 = 21.
  5. Check the result by substituting or estimating: the response should match 21 and make sense in the original problem.

Answer: 21

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