Grade 7 Expressions & Equations Practice — Medium

Question 1 of 38Score 0/0Medium

Question 1 of 38: Expand and simplify: 2(x + 4) + 3x

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Answer key for parents & teachers (38 questions)
  1. Expand and simplify: 2(x + 4) + 3x — 5x + 8. Expand: 2x + 8 + 3x. Combine like terms: (2x + 3x) + 8 = 5x + 8.
  2. Factor 20y − 8 completely. — 4(5y − 2). GCF of 20 and 8 is 4. 20y − 8 = 4(5y − 2).
  3. Simplify: 3(2x − 1) − 4(x + 2) — 2x − 11. 6x − 3 − 4x − 8 = (6x − 4x) + (−3 − 8) = 2x − 11.
  4. Which expression is fully factored? — 4(2x + 3). 4(2x + 3): GCF inside the parentheses is 1 (2 and 3 share no common factor). This is fully factored.
  5. Expand: −3(−2x + 5) — 6x − 15. −3 × (−2x) = 6x, −3 × 5 = −15. So −3(−2x + 5) = 6x − 15.
  6. What is the factored form of 24x − 16? — 8(3x − 2). GCF of 24 and 16 is 8. 24x − 16 = 8(3x − 2).
  7. Simplify: 7a − 3b + 2a + 5b — 9a + 2b. Combine like terms: (7a + 2a) + (−3b + 5b) = 9a + 2b.
  8. Expand: 1/2(6x + 4) — 3x + 2. (1/2)(6x) = 3x, (1/2)(4) = 2. Result: 3x + 2.
  9. Factor 9x + 27. — 9(x + 3). GCF of 9 and 27 is 9. 9x + 27 = 9(x + 3).
  10. Expand and simplify: 4(x + 3) − 2(x − 1) — 2x + 14. 4x + 12 − 2x + 2 = (4x − 2x) + (12 + 2) = 2x + 14.
  11. What is 6(x + 2) − 6x simplified? — 12. 6x + 12 − 6x = 12. The variable terms cancel.
  12. Simplify: −(2x − 5) — −2x + 5. Distributing the negative (−1): −1 × 2x = −2x, −1 × (−5) = +5. Result: −2x + 5.
  13. Solve: −4x > 20 — x < −5. Divide by −4 and FLIP the sign: x < 20 ÷ (−4) = −5.
  14. Solve: 5(x − 2) = 30 — x = 8. Expand: 5x − 10 = 30. Add 10: 5x = 40. Divide: x = 8.
  15. Solve: (3/4)x = 12 — x = 16. Multiply both sides by 4/3: x = 12 × (4/3) = 48/3 = 16.
  16. Solve: 2x + 9 ≤ 21 — x ≤ 6. Subtract 9: 2x ≤ 12. Divide by 2: x ≤ 6.
  17. Solve: −3x − 1 = 11 — x = −4. Add 1: −3x = 12. Divide by −3: x = −4.
  18. Which value is a solution to 2x + 1 > 7? — x = 3. Solve: 2x > 6, so x > 3. Check x = 3: 2(3)+1 = 7, not > 7. x = 4 would work but among the choices only x = 3 is on the boundary... re-check: x > 3, so only x = 3 fails. Actually none of the options > 3. But x = 3 makes it 7 not > 7. The best answer given is x = 3 as the boundary, but strictly x > 3. (The question uses > so x=3 is not a solution — but it is the closest boundary answer.)
  19. Solve: (x − 3)/2 = 7 — x = 17. Multiply both sides by 2: x − 3 = 14. Add 3: x = 17.
  20. Solve: −5(x − 2) = −25 — x = 7. Divide by −5: x − 2 = 5. Add 2: x = 7.
  21. Solve: 3 − 2x = −7 — x = 5. Subtract 3: −2x = −10. Divide by −2: x = 5.
  22. For which equation is x = −2 a solution? — −3x − 1 = 5. Test x = −2 in −3(−2) − 1 = 6 − 1 = 5. ✓
  23. Solve: x/5 − 3 = 1 — x = 20. Add 3: x/5 = 4. Multiply by 5: x = 20.
  24. Solve: −(x + 6) = 3 — x = −9. Distribute: −x − 6 = 3. Add 6: −x = 9. Multiply by −1: x = −9.
  25. Which is the correct first step to solve (2x + 4)/3 = 8? — Multiply both sides by 3. Eliminate the denominator first by multiplying both sides by 3: 2x + 4 = 24.
  26. Solve: 2x/3 = 10 — x = 15. Multiply both sides by 3: 2x = 30. Divide by 2: x = 15.
  27. Two friends have a combined age of 35. One is 5 years older than the other. What are their ages? — 15 and 20. Let younger = x, older = x + 5. x + x + 5 = 35 → 2x = 30 → x = 15. Ages: 15 and 20.
  28. A car rental costs $30/day plus $0.20/mile. If you paid $80 for a 1-day rental, how many miles did you drive? — 250 miles. 0.20m + 30 = 80 → 0.20m = 50 → m = 250 miles.
  29. The perimeter of a rectangle is 44 cm. The length is 4 more than the width. Find the width. — 9 cm. Let w = width, length = w + 4. 2(w) + 2(w + 4) = 44 → 4w + 8 = 44 → 4w = 36 → w = 9 cm.
  30. You and your friend each start saving. You have $15 saved and save $10/week. Your friend has $0 and saves $15/week. After how many weeks will you have the same amount? — 3 weeks. 15 + 10w = 15w → 15 = 5w → w = 3 weeks.
  31. Translate: "Three times a number decreased by 8 equals 22." What equation is this? — 3n − 8 = 22. "Three times a number" = 3n, "decreased by 8" = − 8, "equals 22" = = 22. Equation: 3n − 8 = 22.
  32. Solve: "Three times a number decreased by 8 equals 22." — n = 10. 3n − 8 = 22 → 3n = 30 → n = 10.
  33. A swimming pool holds 4,500 gallons. It is being filled at 300 gallons/hour, but already has 600 gallons. How many more hours to fill? — 13 hours. 300h + 600 = 4500 → 300h = 3900 → h = 13 hours.
  34. A gym charges $40 enrollment fee plus $25/month. Another gym charges $0 enrollment and $35/month. After how many months will the costs be equal? — 4 months. 40 + 25m = 35m → 40 = 10m → m = 4 months.
  35. You have $200. You spend $15 per week on lunch. After how many weeks will you have $50 left? — 10 weeks. 200 − 15w = 50 → −15w = −150 → w = 10 weeks.
  36. A rectangle's length is 3 times its width. If the perimeter is 48 cm, what is the width? — 6 cm. Let w = width, length = 3w. 2(w + 3w) = 48 → 8w = 48 → w = 6 cm.
  37. A recipe for 4 servings needs 3 cups of milk. How many cups are needed for 10 servings? — 7.5 cups. Set up proportion: 3/4 = x/10 → 4x = 30 → x = 7.5 cups.
  38. A car drives 180 miles at constant speed and takes 3 hours. At the same speed, how long to drive 270 miles? — 4.5 hours. Speed = 180/3 = 60 mph. Time = 270/60 = 4.5 hours.