Expressions and Properties
A free Algebra I lesson from the “Algebra Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Algebraic expressions use variables to represent unknown or changing values. Like terms have the same variable part. The distributive property lets you multiply a factor across terms inside parentheses. In Algebra Foundations, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.
What you'll learn
- Identify terms and coefficients
- Apply the distributive property
- Combine like terms
Worked example
Problem. Simplify 3(x + 4) + 2x.
- Distribute 3 across x + 4 to get 3x + 12.
- Combine like terms: 3x + 2x = 5x.
- The simplified expression is 5x + 12.
- Connect the result back to Expressions and Properties so the method and meaning are both clear.
Answer: 5x + 12
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. In 9x - 4, what is the coefficient of x?
Choices: 9 · x · -4 · 5
Show solution
- The coefficient is the number multiplying the variable.
- In 9x, the coefficient is 9.
Answer: 9
2. Simplify 4x + 7x.
Show solution
- Both terms are like terms.
- Add the coefficients: 4 + 7 = 11.
Answer: 11x
3. Simplify 12 - 5 + 3x.
Show solution
- Combine constants: 12 - 5 = 7.
- The variable term stays 3x.
Answer: 3x + 7
4. Simplify 2(x + 5).
Show solution
- Distribute 2 to each term.
- 2 times x is 2x and 2 times 5 is 10.
Answer: 2x + 10
5. Simplify 5(2x - 3).
Show solution
- Distribute 5.
- 5 times 2x is 10x and 5 times -3 is -15.
Answer: 10x - 15
Practice this interactively with instant feedback and an AI tutor.
Practice Expressions and Properties Take the free placement check