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Algebra Readiness Checkpoint

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

This checkpoint mixes the algebra-readiness skills that prepare students for Algebra I: simplifying expressions, solving equations, evaluating powers, and interpreting inequalities. 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

Worked example

Problem. Solve 3x + 4 = 22.

  1. Subtract 4 from both sides: 3x = 18.
  2. Divide both sides by 3.
  3. x = 6.
  4. Connect the calculation back to Algebra Readiness Checkpoint so the method, not just the arithmetic, is clear.

Answer: 6

Practice problems

1. Evaluate 2 + 3^2 x 4.

Show solution
  1. Expression Review: First identify exactly what the question is asking: Evaluate 2 + 3^2 x 4.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Exponent first: 3^2 = 9.
  4. Multiply: 9 x 4 = 36.
  5. Add 2 to get 38.
  6. Check the result by substituting or estimating: the response should match 38 and make sense in the original problem.

Answer: 38

2. Simplify 5x + 2x - 9.

Show solution
  1. Expression Review: First identify exactly what the question is asking: Simplify 5x + 2x - 9.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Combine like terms.
  4. 5x + 2x = 7x.
  5. Check the result by substituting or estimating: the response should match 7x - 9 and make sense in the original problem.

Answer: 7x - 9

3. Evaluate 4a - 5 when a = 6.

Show solution
  1. Expression Review: First identify exactly what the question is asking: Evaluate 4a - 5 when a = 6.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute 6 for a.
  4. 4(6) - 5 = 19.
  5. Check the result by substituting or estimating: the response should match 19 and make sense in the original problem.

Answer: 19

4. Solve x + 14 = 31.

Show solution
  1. Equation Review: First identify exactly what the question is asking: Solve x + 14 = 31.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract 14 from both sides.
  4. x = 17.
  5. Check the result by substituting or estimating: the response should match 17 and make sense in the original problem.

Answer: 17

5. Solve 5n = 45.

Show solution
  1. Equation Review: First identify exactly what the question is asking: Solve 5n = 45.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Divide both sides by 5.
  4. n = 9.
  5. Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.

Answer: 9

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