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7th Math: Expressions & Equations practice questions and exam guide

150 multiple-choice questions and 85 flashcards, organised into 5 chapters, written to the Common Core State Standards blueprint. Every question carries a full rationale.

Last reviewed 2026-10-26 · CoStudy · how we write and review questions

  • 235 total items
  • 150 multiple choice
  • 85 flashcards
  • 5 chapters

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About the 7th Math: Expressions & Equations exam

Common Core State Standards (CCSS) — Mathematics, Grade 7: Expressions and Equations (7.EE.A.1-2, 7.EE.B.3-4). Public standards from corestandards.org.

CoStudy's 7th Math: Expressions & Equations bank holds 235 items organised into 5 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.

What the 7th Math: Expressions & Equations bank covers

Each chapter follows a domain of the published exam outline. Practise one on its own (chapter URLs are in the app and on this page for navigation; they are not sitemap targets):

Free 7th Math: Expressions & Equations practice questions

A sample of 12 multiple-choice questions from the bank, with the full rationale shown.

Solve: 5 − 3x = −7

  1. x = −4
  2. x = −12
  3. x = 12
  4. x = 4

Answer: D — x = 4

D) Subtract 5: −3x = −12; divide by −3: x = 4. A) Sign error. C) Forgot to divide. B) Sign error after dividing.

Simplify: (1/2)(4x − 6)

  1. 2x − 6
  2. 2x − 3
  3. 4x − 3
  4. 2x + 3

Answer: B — 2x − 3

(1/2)(4x) = 2x; (1/2)(−6) = −3 → 2x − 3. (A) only halved x; (C) only halved the constant; (D) sign error on constant.

A car travels at 60 mph for t hours. The distance d is:

  1. d = 60 + t
  2. d = 60 − t
  3. d = 60t
  4. d = t / 60

Answer: C — d = 60t

C) Distance = rate × time. A/B) Added/subtracted units. D) Inverted the relationship.

Solve: 4x − 9 = −1

  1. x = 2
  2. x = −2.5
  3. x = 2.5
  4. x = −2

Answer: A — x = 2

4x = −1 + 9 = 8; x = 2. (B) used 9 − 1 = 8 then divided by −4; (C) same with wrong sign; (D) sign error.

Solve: 3(x + 4) = 21

  1. x = 3
  2. x = 7
  3. x = 9
  4. x = 5

Answer: A — x = 3

A) Distribute: 3x + 12 = 21 → 3x = 9 → x = 3. Alternatively, divide both sides by 3 first. B) Forgot to subtract 12. C) Forgot to divide. D) Random.

Simplify: 4x + 7 − 2x + 3

  1. 2x + 10
  2. 6x + 10
  3. 2x + 4
  4. 6x + 4

Answer: A — 2x + 10

A) 4x − 2x = 2x; 7 + 3 = 10. B) Summed x terms incorrectly. C) Lost a constant. D) Both errors.

A pizza is $12 plus $1.50 per topping. With $19.50, how many toppings?

  1. 4
  2. 13
  3. 6
  4. 5

Answer: D — 5

D) 1.5t + 12 = 19.5 → 1.5t = 7.5 → t = 5. A) Off by one. C) Used 9/1.5. B) Divided 19.5 by 1.5.

Solve: (x − 4)/3 = 2

  1. x = 2
  2. x = 6
  3. x = 10
  4. x = 14

Answer: C — x = 10

C) Multiply by 3: x − 4 = 6; add 4: x = 10. A) Subtracted instead of adding. B) Stopped after multiplying. D) Added 4 then multiplied.

Solve: 3x ≤ 15

  1. x ≤ 5
  2. x ≤ 45
  3. x ≥ 5
  4. x < 5

Answer: A — x ≤ 5

Divide by 3 (positive — no flip): x ≤ 5. (B) multiplied by 3; (C) flipped inequality unnecessarily; (D) changed ≤ to <.

Solve: x/3 + 1 ≥ 4

  1. x ≥ 9
  2. x ≥ 3
  3. x ≥ 15
  4. x ≥ 7

Answer: A — x ≥ 9

x/3 ≥ 3; x ≥ 9. (B) forgot to multiply by 3; (C) multiplied 5 × 3; (D) added 3 and 4.

Inequality 2x + 5 > 13. x =

  1. x > 5
  2. x < 4
  3. x > 9
  4. x > 4

Answer: D — x > 4

D) Subtract 5, divide by 2. A/B/C) Each is incorrect.

Solve: (3x − 6)/2 = 9

  1. x = 4
  2. x = 6
  3. x = 8
  4. x = 12

Answer: C — x = 8

C) Multiply by 2: 3x − 6 = 18; add 6: 3x = 24; x = 8. A) Used 24/(−6). B) Stopped at 18/3. D) Skipped a step.

7th Math: Expressions & Equations flashcards

6 sample cards from the 85 in the bank.

Worked Example: Solve inequality −3x + 4 > 13 (flip the sign).

Step 1: Subtract 4 from both sides: −3x + 4 − 4 > 13 − 4, giving −3x > 9. Step 2: Divide both sides by −3 — NEGATIVE divisor, so FLIP the inequality: −3x/(−3) < 9/(−3), giving x < −3. Step 3: Check with x = −4 (satisfies x < −3): −3(−4) + 4 = 12 + 4 = 16 > 13 ✓. Step 4: Graph — open circle at −3, arrow left. Answer: x < −3.

Combine: 5x + 7x.

12x.

Solve: 3(x − 1) + 4 = 16.

x = 5. (3x − 3 + 4 = 16; 3x + 1 = 16; 3x = 15; x = 5.)

Combine: 0.5x − 0.3 + 2.5x + 1.

3x + 0.7.

Distribute: −3(2x − 4).

−6x + 12.

Solve: −2x > 6.

x < −3. (Flip sign when dividing by −2.)

Practise the full 7th Math: Expressions & Equations bank

These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.

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7th Math: Expressions & Equations — frequently asked

What is the 7th Math: Expressions & Equations exam?

Common Core State Standards (CCSS) — Mathematics, Grade 7: Expressions and Equations (7.EE.A.1-2, 7.EE.B.3-4). Public standards from corestandards.org.

How is CoStudy’s 7th Math: Expressions & Equations bank organised?

It holds 235 items across 5 chapters: Equivalent Linear Expressions; Rewriting Expressions in Different Forms; Multi-Step Real-World Problems; Solving Equations of the Form px + q = r and p(x + q) = r; Solving Multi-Step Inequalities. Free samples on this page include the full rationale, with no account. Chapter counts in the bank are our mix; they are not a promise that the live exam uses the same item counts.

Does CoStudy replace the certifying body?

No. the certifying body owns the outline, the badge, and the sitting rules. This is independent practice with written rationales. We do not sell live items and we do not guarantee a pass.

Where do 7th Math: Expressions & Equations fees, cut scores, and pass rates live?

On the certifying body’s site. CoStudy will not invent a sitting fee or a pass rate. If a table on this page lacks a citation, treat it as unverified.

Are these real 7th Math: Expressions & Equations exam questions?

No. CoStudy does not have live items. The samples below are original practice written to the published outline, with rationales. Anyone selling “real exam dumps” is describing something you should not buy.

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