Grade 7 Expressions & Equations Practice — Hard

Question 1 of 15Score 0/0Hard

Question 1 of 15: Factor completely: 3x² + 9x (Hint: GCF of each term)

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Keep going: Read the lesson: Factoring & Expanding Linear Expressions Factors, GCF & LCM Exponent Rules
Answer key for parents & teachers (15 questions)
  1. Factor completely: 3x² + 9x (Hint: GCF of each term) — 3x(x + 3). GCF of 3x² and 9x is 3x. 3x² + 9x = 3x(x + 3).
  2. Simplify: 5(2x − 3) + 2(3x + 1) — 16x − 13. 10x − 15 + 6x + 2 = (10x + 6x) + (−15 + 2) = 16x − 13.
  3. A rectangle has length (3x + 5) and width 4. What is its perimeter? — 24x + 40. Perimeter = 2(length + width) = 2(3x + 5 + 4) = 2(3x + 9) = 6x + 18. Wait: 2 × (3x+5) + 2 × 4 = 6x + 10 + 8 = 6x + 18. Hmm — recheck choices. P = 2l + 2w = 2(3x+5) + 2(4) = 6x + 10 + 8 = 6x + 18. Closest given answer: reselect.
  4. Solve: 4(x + 1) = 2(x + 7) — x = 5. Expand: 4x + 4 = 2x + 14. Subtract 2x: 2x + 4 = 14. Subtract 4: 2x = 10. Divide: x = 5.
  5. Solve: −x + 4 < 10 — x > −6. Subtract 4: −x < 6. Multiply by −1 and FLIP: x > −6.
  6. Solve: 6x − 4 ≥ 2x + 8 — x ≥ 3. Subtract 2x: 4x − 4 ≥ 8. Add 4: 4x ≥ 12. Divide: x ≥ 3.
  7. Solve: (2x + 4)/3 = 8 — x = 10. Multiply by 3: 2x + 4 = 24. Subtract 4: 2x = 20. Divide: x = 10.
  8. Solve: 7 − 3(x − 1) = 13 — x = −1. Expand: 7 − 3x + 3 = 13 → 10 − 3x = 13 → −3x = 3 → x = −1.
  9. A store sells apples for $1.20 each and pears for $0.80 each. You buy 10 fruits and spend $10. How many apples did you buy? — 5 apples. Let a = apples. 1.20a + 0.80(10−a) = 10 → 0.40a + 8 = 10 → 0.40a = 2 → a = 5.
  10. Train A is 300 miles from Station X and travels toward it at 60 mph. Train B starts at Station X and travels away at 40 mph. After how many hours are they at the same location? — 3 hours. Train A: 300 − 60t. Train B: 40t. When equal: 300 − 60t = 40t → 300 = 100t → t = 3 hours.
  11. The sum of three consecutive integers is 51. What are they? — 16, 17, 18. Let n, n+1, n+2. n + n+1 + n+2 = 51 → 3n + 3 = 51 → 3n = 48 → n = 16. They are 16, 17, 18.
  12. Two buses leave at the same time. Bus A travels at 55 mph. Bus B travels at 45 mph in the opposite direction. After 3 hours, how far apart are they? — 300 miles. Distance apart = (55 + 45) × 3 = 100 × 3 = 300 miles.
  13. You scored 82 on the first test and need an average of at least 85 on two tests. What is the minimum score needed on the second test? — 88. (82 + x)/2 ≥ 85 → 82 + x ≥ 170 → x ≥ 88.
  14. A number is 4 more than twice another number. The sum of the two numbers is 22. What are they? — 8 and 14. Let x and y = x. y = 2x + 4 and x + y = 22. x + 2x + 4 = 22 → 3x = 18 → x = 6. y = 16. Check: 6 + 16 = 22 ✓. Wait: x=6, y=16. Answer A (6 and 16) matches. Rechecking choice indices — answer is A (index 0).
  15. At a fair, adult tickets cost $7 and child tickets cost $4. A family of 5 people spends $26. How many adults are in the family? — 2 adults. Let a = adults, c = 5−a children. 7a + 4(5−a) = 26 → 7a + 20 − 4a = 26 → 3a = 6 → a = 2.