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 = 17
B. x = –3
C. x = 3
D. x = –17
Correct Answer: A
Rationale: Distribute on the right: 3x – 7 = 2x + 10. Subtract 2x from both sides: x
– 7 = 10. Add 7: x = 17. This value checks in the original equation, so the solution
is correct. Choices B and C result from sign errors when transferring terms, and D
reverses the sign of the final constant.
2. Which line has the steepest slope?
A. y = –4x + 9
B. y = 0.5x – 3
,C. y = 2x + 7
D. y = 3
Correct Answer: A
Rationale: The slope is the coefficient of x. Absolute values are 4, 0.5, 2, and 0
respectively. The largest absolute value, 4, occurs in choice A, making it the
steepest. Choice D has zero slope, while B and C have smaller magnitudes.
3. Factor completely: 2x² – 8x – 42
A. 2(x – 3)(x + 7)
B. (2x – 6)(x + 7)
C. 2(x – 7)(x + 3)
D. (x – 7)(2x + 6)
Correct Answer: C
Rationale: First factor out the GCF 2: 2(x² – 4x – 21). Then factor the quadratic to
(x – 7)(x + 3). Thus the complete factorization is 2(x – 7)(x + 3). Choice A
reverses the signs, B does not factor out 2 fully, and D leaves a common factor
inside.
4. Solve the inequality –5x + 2 ≤ 17 and graph the solution on a number line.
A. x ≥ –3
B. x ≤ –3
,C. x ≥ 3
D. x ≤ 3
Correct Answer: A
Rationale: Subtract 2: –5x ≤ 15. Divide by –5, reversing the inequality: x ≥ –3.
Choice B forgets to reverse the inequality sign, while C and D use the wrong
boundary value.
5. Find the zeros of f(x) = x² – 6x + 8
A. –2 and –4
B. 2 and 4
C. 1 and 8
D. –1 and –8
Correct Answer: B
Rationale: Factor: (x – 2)(x – 4) = 0 ⇒ x = 2 or 4. These values make the function
equal zero. Choices A and D keep the correct factors but with incorrect signs, and
C uses factors whose product is 8 but whose sum is not –6.
6. Simplify: (3x²y⁻³)²
A. 9x⁴y⁻⁶
B. 9x⁴y⁻¹
C. 3x⁴y⁻⁵
, D. 6x⁴y⁻⁶
Correct Answer: A
Rationale: Square each factor: 3² = 9, (x²)² = x⁴, (y⁻³)² = y⁻⁶. Thus 9x⁴y⁻⁶. Choice B
adds exponents incorrectly, C forgets to square the coefficient, and D doubles
instead of squaring the 3.
7. A phone plan charges $25 plus $0.08 per minute. Write a function C(m) for
the monthly cost when m minutes are used.
A. C(m) = 25m + 0.08
B. C(m) = 0.08m + 25
C. C(m) = 25 – 0.08m
D. C(m) = 33m
Correct Answer: B
Rationale: The fixed monthly fee is the constant term, and the per-minute charge is
the slope. Therefore C(m) = 0.08m + 25. Choice A reverses the roles of slope and
intercept, C incorrectly subtracts, and D uses an arbitrary product.
8. Solve the system:
2x + 3y = 12
x–y=1
A. (3, 2)
B. (2, 3)
– Complete 70 Questions, Correct
Answers & Detailed Rationales (2025 /
2026 Latest Version)
1. Solve for x: 3x – 7 = 2(x + 5)
A. x = 17
B. x = –3
C. x = 3
D. x = –17
Correct Answer: A
Rationale: Distribute on the right: 3x – 7 = 2x + 10. Subtract 2x from both sides: x
– 7 = 10. Add 7: x = 17. This value checks in the original equation, so the solution
is correct. Choices B and C result from sign errors when transferring terms, and D
reverses the sign of the final constant.
2. Which line has the steepest slope?
A. y = –4x + 9
B. y = 0.5x – 3
,C. y = 2x + 7
D. y = 3
Correct Answer: A
Rationale: The slope is the coefficient of x. Absolute values are 4, 0.5, 2, and 0
respectively. The largest absolute value, 4, occurs in choice A, making it the
steepest. Choice D has zero slope, while B and C have smaller magnitudes.
3. Factor completely: 2x² – 8x – 42
A. 2(x – 3)(x + 7)
B. (2x – 6)(x + 7)
C. 2(x – 7)(x + 3)
D. (x – 7)(2x + 6)
Correct Answer: C
Rationale: First factor out the GCF 2: 2(x² – 4x – 21). Then factor the quadratic to
(x – 7)(x + 3). Thus the complete factorization is 2(x – 7)(x + 3). Choice A
reverses the signs, B does not factor out 2 fully, and D leaves a common factor
inside.
4. Solve the inequality –5x + 2 ≤ 17 and graph the solution on a number line.
A. x ≥ –3
B. x ≤ –3
,C. x ≥ 3
D. x ≤ 3
Correct Answer: A
Rationale: Subtract 2: –5x ≤ 15. Divide by –5, reversing the inequality: x ≥ –3.
Choice B forgets to reverse the inequality sign, while C and D use the wrong
boundary value.
5. Find the zeros of f(x) = x² – 6x + 8
A. –2 and –4
B. 2 and 4
C. 1 and 8
D. –1 and –8
Correct Answer: B
Rationale: Factor: (x – 2)(x – 4) = 0 ⇒ x = 2 or 4. These values make the function
equal zero. Choices A and D keep the correct factors but with incorrect signs, and
C uses factors whose product is 8 but whose sum is not –6.
6. Simplify: (3x²y⁻³)²
A. 9x⁴y⁻⁶
B. 9x⁴y⁻¹
C. 3x⁴y⁻⁵
, D. 6x⁴y⁻⁶
Correct Answer: A
Rationale: Square each factor: 3² = 9, (x²)² = x⁴, (y⁻³)² = y⁻⁶. Thus 9x⁴y⁻⁶. Choice B
adds exponents incorrectly, C forgets to square the coefficient, and D doubles
instead of squaring the 3.
7. A phone plan charges $25 plus $0.08 per minute. Write a function C(m) for
the monthly cost when m minutes are used.
A. C(m) = 25m + 0.08
B. C(m) = 0.08m + 25
C. C(m) = 25 – 0.08m
D. C(m) = 33m
Correct Answer: B
Rationale: The fixed monthly fee is the constant term, and the per-minute charge is
the slope. Therefore C(m) = 0.08m + 25. Choice A reverses the roles of slope and
intercept, C incorrectly subtracts, and D uses an arbitrary product.
8. Solve the system:
2x + 3y = 12
x–y=1
A. (3, 2)
B. (2, 3)
