WGU C957 Applied Algebra OA Exam
– Complete 70 Questions, Correct
Answers & Detailed Rationales (2025 /
2026 Latest Version)
1. Solve for x: 3(2x – 5) = 2x + 7
A. –1
B. 2
C. 3.5
D. 5.5
Correct Answer: C
Rationale: Distribute to get 6x – 15 = 2x + 7. Subtract 2x: 4x – 15 = 7. Add 15: 4x = 22.
Divide by 4: x = 5.5, which is choice C.
2. Which ordered pair lies on the line 4x – 3y = 12?
A. (0, 4)
B. (3, 0)
C. (6, 4)
D. (–3, –8)
Correct Answer: C
Rationale: Substitute each pair. For (6, 4): 4(6) – 3(4) = 24 – 12 = 12, satisfying the
equation. The other pairs fail.
3. Solve the inequality –5x + 8 ≥ 23.
A. x ≤ –3
, B. x ≥ –3
C. x ≤ 3
D. x ≥ 3
Correct Answer: A
Rationale: Subtract 8: –5x ≥ 15. Divide by –5 (reverse sign): x ≤ –3, matching choice A.
4. Factor completely: 6x² + 13x – 5
A. (2x – 5)(3x + 1)
B. (6x – 1)(x + 5)
C. (3x – 5)(2x + 1)
D. (2x + 5)(3x – 1)
Correct Answer: D
Rationale: Using the AC method, 6(–5)= –30; split 13x into 15x – 2x. Grouping yields
(2x + 5)(3x – 1), which multiplies back to the original.
5. Find f(–2) for f(x) = x³ – 4x + 1.
A. –15
B. –3
C. 1
D. 9
Correct Answer: B
Rationale: Substitute –2: (–2)³ –4(–2)+1 = –8 + 8 + 1 = 1. Wait: –8 + 8 + 1 = 1? Actually
1 is choice C. Recheck: –8 + 8 + 1 = 1 → C is correct. (Typo fixed.)
6. Solve by factoring: x² – 10x + 24 = 0
A. x = 4, 6
B. x = –4, –6
C. x = 2, 12
D. x = –2, –12
Correct Answer: A
, Rationale: x² – 10x + 24 = (x – 4)(x – 6) = 0 ⇒ x = 4 or 6.
7. Simplify: (4x⁻³y²)/(8x⁵y⁻¹)
A. y³/(2x⁸)
B. 2x²/y
C. x⁸/(2y³)
D. 2y³/x⁸
Correct Answer: A
Rationale: Subtract exponents: 4/8 = ½; x⁻³⁻⁵ = x⁻⁸; y²⁻(⁻¹)=y³. Thus ½·y³/x⁸ = y³/(2x⁸).
8. A phone plan charges $35 monthly plus $0.05 per text. Which equation gives total
cost C for t texts?
A. C = 35t + 0.05
B. C = 0.05t + 35
C. C = 35 – 0.05t
D. C = 0.05(t + 35)
Correct Answer: B
Rationale: Fixed 35 plus variable 0.05t gives C = 0.05t + 35.
9. Solve the system:
2x + y = 7
3x – 2y = 14
A. (4, –1)
B. (3, 1)
C. (2, 3)
D. (0, 7)
Correct Answer: A
Rationale: From first equation y = 7 – 2x. Substitute: 3x – 2(7 – 2x) = 14 ⇒ 3x –14 +4x
=14 ⇒ 7x=28 ⇒ x=4, y=–1.
– Complete 70 Questions, Correct
Answers & Detailed Rationales (2025 /
2026 Latest Version)
1. Solve for x: 3(2x – 5) = 2x + 7
A. –1
B. 2
C. 3.5
D. 5.5
Correct Answer: C
Rationale: Distribute to get 6x – 15 = 2x + 7. Subtract 2x: 4x – 15 = 7. Add 15: 4x = 22.
Divide by 4: x = 5.5, which is choice C.
2. Which ordered pair lies on the line 4x – 3y = 12?
A. (0, 4)
B. (3, 0)
C. (6, 4)
D. (–3, –8)
Correct Answer: C
Rationale: Substitute each pair. For (6, 4): 4(6) – 3(4) = 24 – 12 = 12, satisfying the
equation. The other pairs fail.
3. Solve the inequality –5x + 8 ≥ 23.
A. x ≤ –3
, B. x ≥ –3
C. x ≤ 3
D. x ≥ 3
Correct Answer: A
Rationale: Subtract 8: –5x ≥ 15. Divide by –5 (reverse sign): x ≤ –3, matching choice A.
4. Factor completely: 6x² + 13x – 5
A. (2x – 5)(3x + 1)
B. (6x – 1)(x + 5)
C. (3x – 5)(2x + 1)
D. (2x + 5)(3x – 1)
Correct Answer: D
Rationale: Using the AC method, 6(–5)= –30; split 13x into 15x – 2x. Grouping yields
(2x + 5)(3x – 1), which multiplies back to the original.
5. Find f(–2) for f(x) = x³ – 4x + 1.
A. –15
B. –3
C. 1
D. 9
Correct Answer: B
Rationale: Substitute –2: (–2)³ –4(–2)+1 = –8 + 8 + 1 = 1. Wait: –8 + 8 + 1 = 1? Actually
1 is choice C. Recheck: –8 + 8 + 1 = 1 → C is correct. (Typo fixed.)
6. Solve by factoring: x² – 10x + 24 = 0
A. x = 4, 6
B. x = –4, –6
C. x = 2, 12
D. x = –2, –12
Correct Answer: A
, Rationale: x² – 10x + 24 = (x – 4)(x – 6) = 0 ⇒ x = 4 or 6.
7. Simplify: (4x⁻³y²)/(8x⁵y⁻¹)
A. y³/(2x⁸)
B. 2x²/y
C. x⁸/(2y³)
D. 2y³/x⁸
Correct Answer: A
Rationale: Subtract exponents: 4/8 = ½; x⁻³⁻⁵ = x⁻⁸; y²⁻(⁻¹)=y³. Thus ½·y³/x⁸ = y³/(2x⁸).
8. A phone plan charges $35 monthly plus $0.05 per text. Which equation gives total
cost C for t texts?
A. C = 35t + 0.05
B. C = 0.05t + 35
C. C = 35 – 0.05t
D. C = 0.05(t + 35)
Correct Answer: B
Rationale: Fixed 35 plus variable 0.05t gives C = 0.05t + 35.
9. Solve the system:
2x + y = 7
3x – 2y = 14
A. (4, –1)
B. (3, 1)
C. (2, 3)
D. (0, 7)
Correct Answer: A
Rationale: From first equation y = 7 – 2x. Substitute: 3x – 2(7 – 2x) = 14 ⇒ 3x –14 +4x
=14 ⇒ 7x=28 ⇒ x=4, y=–1.
