IBEW Aptitude Test Solving Algebraic Equations Questions and Answers 2 — Questions and Answers
Question 1: Solve for x: 5x - 3 = 22
- x = 4
- x = 5 (Correct answer)
- x = 6
- x = 7
Correct answer: x = 5
5x = 22 + 3 = 25. x = 25/5 = 5.
5x - 3 = 22. Add 3 to both sides: 5x = 25. Divide by 5: x = 5. Always verify: 5(5) - 3 = 25 - 3 = 22 ✓. Two-step linear equations are a core algebra skill on the IBEW NJATC aptitude test.
Question 2: Solve: 3(x + 4) = 21
- x = 1
- x = 2
- x = 3 (Correct answer)
- x = 7
Correct answer: x = 3
Distribute: 3x + 12 = 21. 3x = 9. x = 3.
3(x + 4) = 21. Distribute: 3x + 12 = 21. Subtract 12: 3x = 9. Divide by 3: x = 3. Check: 3(3+4) = 3(7) = 21 ✓. Equations with distributive property are standard on IBEW aptitude tests.
Question 3: Solve for y: 4y - 7 = 2y + 9
- y = 7
- y = 8 (Correct answer)
- y = 9
- y = 10
Correct answer: y = 8
4y - 2y = 9 + 7. 2y = 16. y = 8.
Collect y terms: 4y - 2y = 2y. Collect constants: 9 + 7 = 16. So 2y = 16, y = 8. Check: 4(8)-7=25, 2(8)+9=25 ✓. Equations with variables on both sides require collecting like terms — a key IBEW algebra skill.
Question 4: If 2x + 5 = 3x - 1, what is x?
- x = 4
- x = 5
- x = 6 (Correct answer)
- x = 7
Correct answer: x = 6
5 + 1 = 3x - 2x. 6 = x. So x = 6.
2x + 5 = 3x - 1. Subtract 2x: 5 = x - 1. Add 1: 6 = x. So x = 6. Check: 2(6)+5=17, 3(6)-1=17 ✓. This equation requires moving variable terms, a fundamental algebraic manipulation skill.
Question 5: Solve: x/4 + 3 = 7
- x = 12
- x = 14
- x = 16 (Correct answer)
- x = 20
Correct answer: x = 16
x/4 = 7 - 3 = 4. x = 4 × 4 = 16.
x/4 + 3 = 7. Subtract 3: x/4 = 4. Multiply both sides by 4: x = 16. Check: 16/4 + 3 = 4 + 3 = 7 ✓. Equations with fractional coefficients require multiplying both sides by the denominator to clear the fraction.
Question 6: Solve: 2(3x - 1) = 4(x + 3)
- x = 5
- x = 6
- x = 7 (Correct answer)
- x = 8
Correct answer: x = 7
6x - 2 = 4x + 12. 2x = 14. x = 7.
Distribute: 2(3x-1) = 6x-2, 4(x+3) = 4x+12. Equation: 6x-2 = 4x+12. Subtract 4x: 2x-2=12. Add 2: 2x=14. Divide: x=7. Check: 2(21-1)=40, 4(7+3)=40 ✓. Double distribution equations are a common IBEW aptitude test challenge.
IBEW Aptitude Test Solving Algebraic Equations Questions and Answers 2
Solve for x: 5x - 3 = 22