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Algebra I Midterm Exam

A free Algebra I lesson from the “Systems of Linear Equations and Inequalities” unit, with a worked example and practice problems including step-by-step solutions.

The midterm reviews the first half of Algebra I: expressions, equations, inequalities, formulas, functions, slope, linear equations, systems, and systems word problems. Problems are mixed so students must identify the structure before choosing a method. In Systems of Linear Equations and Inequalities, 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

Why it matters: Algebra I assessments mix symbolic fluency with modeling, graph interpretation, and strategy choice so students practice the same switching they need on cumulative tests.

Worked example

Problem. Worked example from Expressions and Properties: In 9x - 4, what is the coefficient of x?

  1. Warm-up: First identify exactly what the question is asking: In 9x - 4, 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 9x, the coefficient is 9.

Answer: 9

Practice problems

1. Algebra I Midterm Exam review case A from Expressions and Properties: In 9x - 4, what is the coefficient of x?

Choices: 9 · x · -4 · 5

Show solution
  1. Warm-up: First identify exactly what the question is asking: In 9x - 4, 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 9x, the coefficient is 9.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 9

2. Algebra I Midterm Exam review case B from Expressions and Properties: Simplify 4x + 7x.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Simplify 4x + 7x.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Both terms are like terms.
  4. Add the coefficients: 4 + 7 = 11.
  5. Check the result by substituting or estimating: the response should match 11x and make sense in the original problem.

Answer: 11x

3. Algebra I Midterm Exam review case C from Expressions and Properties: Simplify 12 - 5 + 3x.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Simplify 12 - 5 + 3x.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Combine constants: 12 - 5 = 7.
  4. The variable term stays 3x.
  5. Check the result by substituting or estimating: the response should match 3x + 7 and make sense in the original problem.

Answer: 3x + 7

4. Algebra I Midterm Exam review case D from Expressions and Properties: Simplify 2(x + 5).

Show solution
  1. Core Practice: First identify exactly what the question is asking: Simplify 2(x + 5).
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Distribute 2 to each term.
  4. 2 times x is 2x and 2 times 5 is 10.
  5. Check the result by substituting or estimating: the response should match 2x + 10 and make sense in the original problem.

Answer: 2x + 10

5. Algebra I Midterm Exam review case E from Expressions and Properties: Simplify 5(2x - 3).

Show solution
  1. Core Practice: First identify exactly what the question is asking: Simplify 5(2x - 3).
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Distribute 5.
  4. 5 times 2x is 10x and 5 times -3 is -15.
  5. Check the result by substituting or estimating: the response should match 10x - 15 and make sense in the original problem.

Answer: 10x - 15

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