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.
What you'll learn
- Identify terms, coefficients, and variables
- Evaluate expressions by substitution
- Combine like terms
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.
- Substitute 4 for x.
- 3x becomes 3 x 4 = 12.
- 12 + 5 = 17.
Answer: 17
Practice problems
1. Evaluate x + 8 when x = 6.
Show solution
- Warm-up: First identify exactly what the question is asking: Evaluate x + 8 when x = 6.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Substitute 6 for x.
- 6 + 8 = 14.
- 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
- Warm-up: First identify exactly what the question is asking: Evaluate 5a when a = 3.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- 5a means 5 times a.
- 5 x 3 = 15.
- 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
- Warm-up: First identify exactly what the question is asking: In 7x + 2, what is the coefficient of x?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- The coefficient is the number multiplying the variable.
- In 7x, the coefficient is 7.
- 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
- Core Practice: First identify exactly what the question is asking: Evaluate 2x + 9 when x = 5.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Substitute 5 for x.
- 2 x 5 + 9 = 10 + 9 = 19.
- 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
- Core Practice: First identify exactly what the question is asking: Evaluate 4n - 3 when n = 8.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Substitute 8 for n.
- 4 x 8 - 3 = 32 - 3 = 29.
- 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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