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Expressions and Substitution

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

An expression can contain numbers, variables, and operations. To evaluate an expression, substitute a number for the variable and then simplify. Like terms have the same variable part, so they can be combined. 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

Why it matters: Spreadsheet formulas, coding expressions, and tax tables all use variables to stand in for changing numbers. Substituting a value is how a general rule becomes a specific answer.

Worked example

Problem. Evaluate 3x + 5 when x = 4.

  1. Substitute 4 for x.
  2. 3x becomes 3 x 4 = 12.
  3. 12 + 5 = 17.
  4. Connect the calculation back to Expressions and Substitution so the method, not just the arithmetic, is clear.

Answer: 17

Practice problems

1. Evaluate x + 8 when x = 6.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Evaluate x + 8 when x = 6.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute 6 for x.
  4. 6 + 8 = 14.
  5. Check the result by substituting or estimating: the response should match 14 and make sense in the original problem.

Answer: 14

2. Evaluate 5a when a = 3.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Evaluate 5a when a = 3.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. 5a means 5 times a.
  4. 5 x 3 = 15.
  5. Check the result by substituting or estimating: the response should match 15 and make sense in the original problem.

Answer: 15

3. In 7x + 2, what is the coefficient of x?

Choices: 7 · x · 2 · 9

Show solution
  1. Warm-up: First identify exactly what the question is asking: In 7x + 2, what is the coefficient of x?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The coefficient is the number multiplying the variable.
  4. In 7x, the coefficient is 7.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 7

4. Evaluate 2x + 9 when x = 5.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Evaluate 2x + 9 when x = 5.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute 5 for x.
  4. 2 x 5 + 9 = 10 + 9 = 19.
  5. Check the result by substituting or estimating: the response should match 19 and make sense in the original problem.

Answer: 19

5. Evaluate 4n - 3 when n = 8.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Evaluate 4n - 3 when n = 8.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute 8 for n.
  4. 4 x 8 - 3 = 32 - 3 = 29.
  5. Check the result by substituting or estimating: the response should match 29 and make sense in the original problem.

Answer: 29

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