WGU C957 Applied Algebra OA Exam
– Complete 70 Questions, Correct
Answers & Detailed Rationales (2025 /
2026 Latest Version)
1. Solve for x: 3x − 7 = 2(x + 5)
A. x = 3
B. x = 7
C. x = 13
D. x = 17
Correct Answer: D
Rationale: Distribute on the right: 3x − 7 = 2x + 10. Subtract 2x from both sides: x
− 7 = 10. Add 7: x = 17. Choice A results from subtracting 2x incorrectly on the
left. Choice B forgets to distribute the 2. Choice C adds 7 to the wrong side.
2. Which slope corresponds to a line perpendicular to y = −4x + 9?
A. −4
B. 1/4
C. 4
D. −1/4
Correct Answer: B
Rationale: Perpendicular slopes are opposite reciprocals. The given slope is −4, so
the perpendicular slope is 1/4. Choice A is the original slope. Choice C is the
,negative, not reciprocal. Choice D is the opposite sign but still reciprocal
magnitude.
3. Solve the inequality 5 − 2x ≥ 11 and graph the solution.
A. x ≤ −3
B. x ≥ −3
C. x ≤ 3
D. x ≥ 3
Correct Answer: A
Rationale: Subtract 5: −2x ≥ 6. Divide by −2 (reverse inequality): x ≤ −3. Choice B
forgets to reverse the sign. Choices C and D use wrong direction or magnitude.
4. Factor completely: 6x² + 15x
A. 3x(2x + 5)
B. 3(2x² + 5x)
C. x(6x + 15)
D. 6x(x + 5)
Correct Answer: A
Rationale: Greatest common factor is 3x, giving 3x(2x + 5). Choice B leaves x
un-factored. Choice C fails to factor out 3. Choice D loses the factor 3.
5. Find f(−2) for f(x) = x² − 3x + 4
A. 2
B. 6
C. 14
D. 18
Correct Answer: C
, Rationale: Substitute −2: (−2)² −3(−2) + 4 = 4 + 6 + 4 = 14. Choice A squares
incorrectly. Choice B drops the last term. Choice D doubles the middle term sign.
6. Solve x² = 49
A. x = 7 only
B. x = ±7
C. x = 0
D. x = 24.5
Correct Answer: B
Rationale: Square-root property gives both positive and negative roots. Choice A
omits the negative root. Choices C and D divide instead of root.
7. A rectangle’s length is 4 cm more than twice its width. If the perimeter is 56
cm, find the width.
A. 8 cm
B. 10 cm
C. 12 cm
D. 20 cm
Correct Answer: A
Rationale: Let width = w, length = 2w + 4. Perimeter: 2(w + 2w + 4) = 56 → 6w +
8 = 56 → w = 8. Choice B solves length instead. Choices C and D miscalculate
distribution.
8. Simplify (2x³y⁻²)³
A. 6x⁹y⁻⁵
B. 8x⁶y⁻⁵
C. 8x⁹y⁻⁶
D. 6x⁹y⁻⁶
Correct Answer: C
– Complete 70 Questions, Correct
Answers & Detailed Rationales (2025 /
2026 Latest Version)
1. Solve for x: 3x − 7 = 2(x + 5)
A. x = 3
B. x = 7
C. x = 13
D. x = 17
Correct Answer: D
Rationale: Distribute on the right: 3x − 7 = 2x + 10. Subtract 2x from both sides: x
− 7 = 10. Add 7: x = 17. Choice A results from subtracting 2x incorrectly on the
left. Choice B forgets to distribute the 2. Choice C adds 7 to the wrong side.
2. Which slope corresponds to a line perpendicular to y = −4x + 9?
A. −4
B. 1/4
C. 4
D. −1/4
Correct Answer: B
Rationale: Perpendicular slopes are opposite reciprocals. The given slope is −4, so
the perpendicular slope is 1/4. Choice A is the original slope. Choice C is the
,negative, not reciprocal. Choice D is the opposite sign but still reciprocal
magnitude.
3. Solve the inequality 5 − 2x ≥ 11 and graph the solution.
A. x ≤ −3
B. x ≥ −3
C. x ≤ 3
D. x ≥ 3
Correct Answer: A
Rationale: Subtract 5: −2x ≥ 6. Divide by −2 (reverse inequality): x ≤ −3. Choice B
forgets to reverse the sign. Choices C and D use wrong direction or magnitude.
4. Factor completely: 6x² + 15x
A. 3x(2x + 5)
B. 3(2x² + 5x)
C. x(6x + 15)
D. 6x(x + 5)
Correct Answer: A
Rationale: Greatest common factor is 3x, giving 3x(2x + 5). Choice B leaves x
un-factored. Choice C fails to factor out 3. Choice D loses the factor 3.
5. Find f(−2) for f(x) = x² − 3x + 4
A. 2
B. 6
C. 14
D. 18
Correct Answer: C
, Rationale: Substitute −2: (−2)² −3(−2) + 4 = 4 + 6 + 4 = 14. Choice A squares
incorrectly. Choice B drops the last term. Choice D doubles the middle term sign.
6. Solve x² = 49
A. x = 7 only
B. x = ±7
C. x = 0
D. x = 24.5
Correct Answer: B
Rationale: Square-root property gives both positive and negative roots. Choice A
omits the negative root. Choices C and D divide instead of root.
7. A rectangle’s length is 4 cm more than twice its width. If the perimeter is 56
cm, find the width.
A. 8 cm
B. 10 cm
C. 12 cm
D. 20 cm
Correct Answer: A
Rationale: Let width = w, length = 2w + 4. Perimeter: 2(w + 2w + 4) = 56 → 6w +
8 = 56 → w = 8. Choice B solves length instead. Choices C and D miscalculate
distribution.
8. Simplify (2x³y⁻²)³
A. 6x⁹y⁻⁵
B. 8x⁶y⁻⁵
C. 8x⁹y⁻⁶
D. 6x⁹y⁻⁶
Correct Answer: C
