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52 multiple-choice questions and 17 flashcards on Solving Equations of the Form px + q = r and p(x + q) = r, about 35% of the 7th Math: Expressions & Equations bank. Every one carries a written rationale.
Solving Equations of the Form px + q = r and p(x + q) = r is one of 5 chapters in CoStudy's 7th Math: Expressions & Equations bank, and it holds 52 of the bank's 150 multiple-choice questions — roughly 35% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
Solve: 7 − 2x = 1
Answer: A — x = 3
A) Subtract 7: −2x = −6; divide by −2: x = 3. B) Sign error after dividing. C) Used 7 + 1 = 8. D) Sign error throughout.
Solve: (2/3)x = 6
Answer: D — x = 9
Multiply by reciprocal 3/2: x = 6 × (3/2) = 9. Check: (2/3)(9) = 6 ✓. (A) divided by 2 only; (C) multiplied by 2; (B) divided 6 by 3.
Solve: −4(x − 5) = 8
Answer: A — x = 3
x − 5 = −2 (divide by −4); x = 3. Check: −4(3 − 5) = −4(−2) = 8 ✓. (B) used +4; (C) subtracted 5 from −2; (D) sign errors.
Solve: x/3 + 5 = 11
Answer: B — x = 18
B) Subtract 5: x/3 = 6; multiply by 3: x = 18. A) Divided 6 by 3 instead of multiplying. C) Multiplied 16 × 3 — forgot to subtract 5 first. D) Stopped at x/3 = 6.
Simplify: 4(3x − 1) − 2(x + 5)
Answer: A — 10x − 14
12x − 4 − 2x − 10 = 10x − 14. (B) sign error on −10 → got +6; (C) forgot to subtract 2x; (D) arithmetic on x terms.
Alex has $20 more than 3 times Ben's amount. Alex has $53. How much does Ben have?
Answer: A — $11
3b + 20 = 53 → 3b = 33 → b = $11. (B) added 20 incorrectly; (C) used different multiplier; (D) divided 53 by 3 without subtracting.
Solve: 3(x + 4) = 21
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.
Solve: x − 7 = −3
Answer: B — x = 4
Add 7: x = −3 + 7 = 4. (A) subtracted 7; (C/D) sign errors.
Solve: −x/2 + 3 = 7
Answer: B — x = −8
B) Subtract 3: −x/2 = 4; multiply by −2: x = −8. A) Forgot the negative. C) Wrong arithmetic. D) Sign error from arithmetic.
A shirt costs $12 with 8% tax. Which expression gives the total cost?
Answer: C — 12(1.08)
Total = price × (1 + tax rate) = 12 × 1.08. (A) adds 8 directly (wrong); (B) gives only the tax amount; (D) divides.
4 cards from the 17 in this chapter.
Solve: 6(x + 2) = −18.
x = −5.
Solve: 2(x + 3) = 14.
x = 4. (Distribute: 2x + 6 = 14; or divide first: x + 3 = 7; x = 4.)
Worked Example: Solve −2x + 9 = 3.
Step 1: Subtract 9 from both sides: −2x + 9 − 9 = 3 − 9, giving −2x = −6. Step 2: Divide both sides by −2 — negative ÷ negative is positive: −2x/(−2) = −6/(−2), giving x = 3. Step 3: Check: −2(3) + 9 = −6 + 9 = 3 ✓. Answer: x = 3.
Solve: −5(x − 2) = 15.
x = −1. (x − 2 = −3; x = −1.)
These are a sample. The full Solving Equations of the Form px + q = r and p(x + q) = r chapter runs 69 items with per-chapter progress tracking, on the web and in the iOS app.
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