IBEW Solving Algebraic Equations 2 — Questions and Answers
Question 1: Solve for x: 5x - 3 = 2x + 12
- x = 4
- x = 5 (Correct answer)
- x = 3
- x = 6
Correct answer: x = 5
5x - 2x = 12 + 3 → 3x = 15 → x = 5.
5x - 3 = 2x + 12. Subtract 2x from both sides: 3x - 3 = 12. Add 3 to both sides: 3x = 15. Divide by 3: x = 5. Check: 5(5) - 3 = 22 and 2(5) + 12 = 22 ✓.
Question 2: Solve: 2(x + 4) = 3(x - 1)
- x = 9
- x = 10
- x = 11 (Correct answer)
- x = 8
Correct answer: x = 11
2x + 8 = 3x - 3 → 8 + 3 = 3x - 2x → x = 11.
Distribute: 2x + 8 = 3x - 3. Subtract 2x from both sides: 8 = x - 3. Add 3 to both sides: x = 11. Check: 2(11+4) = 2(15) = 30 and 3(11-1) = 3(10) = 30 ✓.
Question 3: Solve the inequality: 4x + 7 > 19
- x > 2
- x > 3 (Correct answer)
- x < 3
- x ≥ 3
Correct answer: x > 3
4x > 12 → x > 3.
4x + 7 > 19. Subtract 7: 4x > 12. Divide by 4 (positive, so inequality direction stays): x > 3. Any value greater than 3 satisfies the inequality.
Question 4: Solve for y: y/3 + 5 = 9
- y = 10
- y = 11
- y = 12 (Correct answer)
- y = 14
Correct answer: y = 12
y/3 = 4 → y = 12.
y/3 + 5 = 9. Subtract 5 from both sides: y/3 = 4. Multiply both sides by 3: y = 12. Check: 12/3 + 5 = 4 + 5 = 9 ✓.
Question 5: Solve: 3x² = 75
- x = ±4
- x = ±5 (Correct answer)
- x = ±6
- x = ±25
Correct answer: x = ±5
x² = 25 → x = ±5.
3x² = 75. Divide by 3: x² = 25. Take square root: x = ±√25 = ±5. Both x = 5 and x = -5 are solutions because both squared equal 25.
Question 6: Solve: (x - 2)/4 = (x + 1)/3
- x = -10 (Correct answer)
- x = 10
- x = -8
- x = 8
Correct answer: x = -10
Cross multiply: 3(x-2) = 4(x+1) → 3x - 6 = 4x + 4 → -x = 10 → x = -10.
Cross multiply: 3(x - 2) = 4(x + 1). Distribute: 3x - 6 = 4x + 4. Subtract 3x: -6 = x + 4. Subtract 4: x = -10. Check: (-10-2)/4 = -12/4 = -3 and (-10+1)/3 = -9/3 = -3 ✓.
IBEW Solving Algebraic Equations 2
Solve for x: 5x - 3 = 2x + 12