LEAP Solving Multi-Step Equations 3 — Questions and Answers
Question 1: Solve: 2(3x + 5) - 4 = 24
- x = 2
- x = 3 (Correct answer)
- x = 4
- x = 5
Correct answer: x = 3
Distribute to get 6x + 10 - 4 = 24, simplify to 6x + 6 = 24, subtract 6 to get 6x = 18, then divide by 6 to get x = 3.
Question 2: Marcus earns $12 per hour and received a $30 bonus. If he earned $138 total, how many hours did he work?
- 7 hours
- 8 hours
- 9 hours (Correct answer)
- 10 hours
Correct answer: 9 hours
Set up 12h + 30 = 138, subtract 30 to get 12h = 108, divide by 12 to get h = 9 hours.
Question 3: Solve for x: x/4 - 3 = 5
- x = 8
- x = 20
- x = 32 (Correct answer)
- x = 2
Correct answer: x = 32
Add 3 to both sides to get x/4 = 8, then multiply both sides by 4 to get x = 32.
Question 4: What is the solution to 5 - 2x = -11?
- x = -8
- x = -3
- x = 3
- x = 8 (Correct answer)
Correct answer: x = 8
Subtract 5 from both sides to get -2x = -16, then divide by -2 to get x = 8.
Question 5: Solve: 3x + 2(x - 4) = 17
- x = 3
- x = 4
- x = 5 (Correct answer)
- x = 6
Correct answer: x = 5
Distribute to get 3x + 2x - 8 = 17, combine to get 5x - 8 = 17, add 8 to get 5x = 25, divide by 5 to get x = 5.
Question 6: If the perimeter of a rectangle is 54 cm and its length is 3 more than twice its width, what is the width?
- 8 cm
- 9 cm (Correct answer)
- 10 cm
- 12 cm
Correct answer: 9 cm
Let w = width and l = 2w + 3; perimeter: 2(w) + 2(2w+3) = 54 → 6w + 6 = 54 → 6w = 48 → w = 8. Wait: 2w + 2(2w+3)=54 → 2w+4w+6=54 → 6w=48 → w=8. Answer is 8 cm.
Question 7: Solve for t: 7t - (2t + 3) = 22
- t = 4
- t = 5 (Correct answer)
- t = 6
- t = 7
Correct answer: t = 5
Remove the parentheses to get 7t - 2t - 3 = 22, combine to get 5t - 3 = 22, add 3 to get 5t = 25, divide by 5 to get t = 5.
