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
- Solve equations with variables and constants
- Use distribution before solving
- Recognize equations with no solution or all solutions
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.
- Subtract 7 from both sides: 2x = 12.
- Divide both sides by 2.
- x = 6.
Answer: 6
Practice problems
1. Solve 3x + 5 = 20.
Show solution
- Warm-up: First identify exactly what the question is asking: Solve 3x + 5 = 20.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Subtract 5 from both sides: 3x = 15.
- Divide by 3: x = 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
- Warm-up: First identify exactly what the question is asking: Solve 4x - 9 = 15.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Add 9 to both sides: 4x = 24.
- Divide by 4: x = 6.
- 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
- Warm-up: First identify exactly what the question is asking: What is the first step for 5x + 8 = 33?
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Undo the +8 before dividing.
- Subtract 8 from both sides.
- 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
- Core Practice: First identify exactly what the question is asking: Solve 7x + 2 = 44.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Subtract 2: 7x = 42.
- Divide by 7: x = 6.
- 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
- Core Practice: First identify exactly what the question is asking: Solve 9 - 2x = 21.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Subtract 9 from both sides: -2x = 12.
- Divide by -2: x = -6.
- 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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