WGU C957 Applied Algebra OA Exam – Complete
70 Questions, Correct Answers & Detailed
Rationales (2025 Latest Version)
1. Solve for x: 3x − 7 = 2(x + 4)
A. x = 1
B. x = 5
C. x = 9
D. x = 15
Correct Answer: D
Rationale: Distribute on the right: 3x − 7 = 2x + 8. Subtract 2x from both
sides: x − 7 = 8. Add 7: x = 15. Choices A, B, and C result from arithmetic
slips such as sign errors or incomplete distribution.
2. Which slope corresponds to a line perpendicular to y = − 2/5 x + 3?
A. 5/2
B. −5/2
C. 2/5
D. −2/5
Correct Answer: A
Rationale: Perpendicular slopes are opposite reciprocals. The negative
reciprocal of −2/5 is 5/2. Options B and C keep the wrong sign or invert
incorrectly, while D repeats the original slope.
, 3. Solve the inequality 4 − 3x ≤ 10 and graph the solution.
A. x ≥ −2
B. x ≤ −2
C. x ≥ 2
D. x ≤ 2
Correct Answer: A
Rationale: Subtract 4: −3x ≤ 6. Divide by −3 and reverse the symbol: x ≥ −2.
Choices B and D fail to reverse the inequality, and C solves for the wrong
boundary.
4. Factor completely: 6x² + 7x − 20
A. (2x − 5)(3x + 4)
B. (2x + 5)(3x − 4)
C. (6x − 5)(x + 4)
D. (3x − 5)(2x + 4)
Correct Answer: B
Rationale: AC = −120; find factors −8 and 15 whose sum is 7. Rewrite: 6x² −
8x + 15x − 20, group, and factor to (2x + 5)(3x − 4). Other pairs give middle
terms of 7x only when signs and placement match B.
5. Find f(−3) for f(x) = x² − 5x + 2.
A. −4
B. 26
C. 8
D. 14
Correct Answer: B
, Rationale: Substitute −3: (−3)² −5(−3) + 2 = 9 + 15 + 2 = 26. Choice A
forgets to square, C miscalculates the middle term, and D drops the sign on
the last term.
6. Solve by factoring: x² − 9x + 18 = 0
A. x = 3, 6
B. x = −3, −6
C. x = 2, 9
D. x = −2, −9
Correct Answer: A
Rationale: Factors as (x − 3)(x − 6) = 0 → x = 3 or 6. Negative pairs in B and
D produce positive middle terms, while C gives +11x.
7. Simplify: (2x³y⁻²)³
A. 6x⁹y⁻⁵
B. 8x⁶y⁻⁵
C. 8x⁹y⁻⁶
D. 6x⁹y⁻⁶
Correct Answer: C
Rationale: Power of product: 2³ = 8, (x³)³ = x⁹, (y⁻²)³ = y⁻⁶. Choice A and D err
with coefficients; B mishandles the y exponent.
8. Solve the system:
2x + y = 7
x − y = −1
A. (2, 3)
B. (3, 1)
70 Questions, Correct Answers & Detailed
Rationales (2025 Latest Version)
1. Solve for x: 3x − 7 = 2(x + 4)
A. x = 1
B. x = 5
C. x = 9
D. x = 15
Correct Answer: D
Rationale: Distribute on the right: 3x − 7 = 2x + 8. Subtract 2x from both
sides: x − 7 = 8. Add 7: x = 15. Choices A, B, and C result from arithmetic
slips such as sign errors or incomplete distribution.
2. Which slope corresponds to a line perpendicular to y = − 2/5 x + 3?
A. 5/2
B. −5/2
C. 2/5
D. −2/5
Correct Answer: A
Rationale: Perpendicular slopes are opposite reciprocals. The negative
reciprocal of −2/5 is 5/2. Options B and C keep the wrong sign or invert
incorrectly, while D repeats the original slope.
, 3. Solve the inequality 4 − 3x ≤ 10 and graph the solution.
A. x ≥ −2
B. x ≤ −2
C. x ≥ 2
D. x ≤ 2
Correct Answer: A
Rationale: Subtract 4: −3x ≤ 6. Divide by −3 and reverse the symbol: x ≥ −2.
Choices B and D fail to reverse the inequality, and C solves for the wrong
boundary.
4. Factor completely: 6x² + 7x − 20
A. (2x − 5)(3x + 4)
B. (2x + 5)(3x − 4)
C. (6x − 5)(x + 4)
D. (3x − 5)(2x + 4)
Correct Answer: B
Rationale: AC = −120; find factors −8 and 15 whose sum is 7. Rewrite: 6x² −
8x + 15x − 20, group, and factor to (2x + 5)(3x − 4). Other pairs give middle
terms of 7x only when signs and placement match B.
5. Find f(−3) for f(x) = x² − 5x + 2.
A. −4
B. 26
C. 8
D. 14
Correct Answer: B
, Rationale: Substitute −3: (−3)² −5(−3) + 2 = 9 + 15 + 2 = 26. Choice A
forgets to square, C miscalculates the middle term, and D drops the sign on
the last term.
6. Solve by factoring: x² − 9x + 18 = 0
A. x = 3, 6
B. x = −3, −6
C. x = 2, 9
D. x = −2, −9
Correct Answer: A
Rationale: Factors as (x − 3)(x − 6) = 0 → x = 3 or 6. Negative pairs in B and
D produce positive middle terms, while C gives +11x.
7. Simplify: (2x³y⁻²)³
A. 6x⁹y⁻⁵
B. 8x⁶y⁻⁵
C. 8x⁹y⁻⁶
D. 6x⁹y⁻⁶
Correct Answer: C
Rationale: Power of product: 2³ = 8, (x³)³ = x⁹, (y⁻²)³ = y⁻⁶. Choice A and D err
with coefficients; B mishandles the y exponent.
8. Solve the system:
2x + y = 7
x − y = −1
A. (2, 3)
B. (3, 1)
