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.
What you'll learn
- Use inverse operations
- Isolate the variable
- Check a solution by substitution
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.
- The variable has 7 subtracted from it.
- Undo subtraction by adding 7 to both sides.
- x = 22. Check: 22 - 7 = 15.
Answer: 22
Practice problems
1. Solve x + 9 = 24.
Show solution
- Warm-up: First identify exactly what the question is asking: Solve x + 9 = 24.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Subtract 9 from both sides.
- 24 - 9 = 15.
- 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
- Warm-up: First identify exactly what the question is asking: Solve y - 6 = 11.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Add 6 to both sides.
- 11 + 6 = 17.
- 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
- Warm-up: First identify exactly what the question is asking: Solve 4x = 28.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Undo multiplication by dividing by 4.
- 28 divided by 4 equals 7.
- 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
- Core Practice: First identify exactly what the question is asking: Solve n/5 = 6.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Undo division by multiplying both sides by 5.
- 6 x 5 = 30.
- 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
- Core Practice: First identify exactly what the question is asking: Solve a - 13 = 8.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Add 13 to both sides.
- 8 + 13 = 21.
- 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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