CMClearMathAcademy

Algebra Foundations Checkpoint

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

This checkpoint closes the Algebra Foundations unit with mixed expressions, equations, inequalities, formulas, and rearranging. The goal is to choose the right algebra move without being told the lesson name.

What you'll learn

Why it matters: Mixed algebra checks feel like real planning work: one task may need simplification, another an equation, and another a formula rearranged before any numbers make sense.

Worked example

Problem. Solve 4(x - 2) + 3 = 23.

  1. Subtract 3 from both sides: 4(x - 2) = 20.
  2. Divide by 4: x - 2 = 5.
  3. Add 2, so x = 7.

Answer: 7

Practice problems

1. Simplify 5(x + 2) - 3x.

Show solution
  1. Expressions: First identify exactly what the question is asking: Simplify 5(x + 2) - 3x.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Distribute 5 to get 5x + 10.
  4. Combine 5x - 3x = 2x.
  5. Check the result by substituting or estimating: the response should match 2x + 10 and make sense in the original problem.

Answer: 2x + 10

2. Evaluate 3a - 7 when a = 9.

Show solution
  1. Expressions: First identify exactly what the question is asking: Evaluate 3a - 7 when a = 9.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute 9 for a.
  4. 3(9) - 7 = 20.
  5. Check the result by substituting or estimating: the response should match 20 and make sense in the original problem.

Answer: 20

3. Solve 6x - 5 = 31.

Show solution
  1. Equations: First identify exactly what the question is asking: Solve 6x - 5 = 31.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Add 5: 6x = 36.
  4. Divide by 6: x = 6.
  5. Check the result by substituting or estimating: the response should match 6 and make sense in the original problem.

Answer: 6

4. Solve 3(x + 4) = 30.

Show solution
  1. Equations: First identify exactly what the question is asking: Solve 3(x + 4) = 30.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Divide by 3: x + 4 = 10.
  4. Subtract 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

5. What kind of equation is 2x + 5 = 2x + 1?

Choices: No solution · All real numbers · x = 4 only · x = 0 only

Show solution
  1. Equations: First identify exactly what the question is asking: What kind of equation is 2x + 5 = 2x + 1?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract 2x from both sides.
  4. 5 = 1 is false.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: No solution

Practice this interactively with instant feedback and an AI tutor.

Practice Algebra Foundations Checkpoint Take the free placement check

More Algebra I lessons