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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.

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.

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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