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
- Identify terms, coefficients, and variables
- Evaluate expressions by substitution
- Combine like terms
Worked example
Problem. Evaluate 3x + 5 when x = 4.
- Substitute 4 for x.
- 3x becomes 3 x 4 = 12.
- 12 + 5 = 17.
- Connect the calculation back to Expressions and Substitution so the method, not just the arithmetic, is clear.
Answer: 17
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Evaluate x + 8 when x = 6.
Show solution
- Substitute 6 for x.
- 6 + 8 = 14.
Answer: 14
2. Evaluate 5a when a = 3.
Show solution
- 5a means 5 times a.
- 5 x 3 = 15.
Answer: 15
3. In 7x + 2, what is the coefficient of x?
Choices: 7 · x · 2 · 9
Show solution
- The coefficient is the number multiplying the variable.
- In 7x, the coefficient is 7.
Answer: 7
4. Evaluate 2x + 9 when x = 5.
Show solution
- Substitute 5 for x.
- 2 x 5 + 9 = 10 + 9 = 19.
Answer: 19
5. Evaluate 4n - 3 when n = 8.
Show solution
- Substitute 8 for n.
- 4 x 8 - 3 = 32 - 3 = 29.
Answer: 29
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