WGU C957 Applied Algebra OA Exam –
Complete 70 Questions, Correct Answers
& Detailed Rationales ( Latest
Version)
1. Solve for x: 3x – 7 = 2(x + 4)
A. x = 5
B. x = 8
C. x = 15
D. x = 1
Correct Answer: C
Rationale: Distribute on the right: 3x – 7 = 2x + 8. Subtract 2x from both sides: x – 7 = 8. Add 7:
x = 15. Choice A results from adding 7 too early, B from dropping the negative, and D from
subtracting 2x incorrectly.
2. Which slope corresponds to the line through (–2, 5) and (4, –1)?
A. –1
B. 1
C. –2
D. 0
,Correct Answer: A
Rationale: Slope m = (y₂ – y₁)/(x₂ – x₁) = (–1 – 5)/(4 – (–2)) = –6/6 = –1. Choice B reverses the
subtraction order, C miscalculates the denominator, and D ignores the y-change.
3. Solve |2x – 5| ≤ 9 and express the solution in interval notation.
A. [–2, 7]
B. (–∞, –2] ∪ [7, ∞)
C. [–7, 2]
D. (–2, 7)
Correct Answer: A
Rationale: Absolute-value inequality becomes –9 ≤ 2x – 5 ≤ 9. Add 5: –4 ≤ 2x ≤ 14. Divide by 2:
–2 ≤ x ≤ 7. Choice B reflects the wrong “or” case, C reverses endpoints, and D uses incorrect
openness.
4. Factor completely: 6x² + 13x – 5
A. (2x – 1)(3x + 5)
B. (6x – 1)(x + 5)
C. (3x – 1)(2x + 5)
D. (2x + 1)(3x – 5)
Correct Answer: C
Rationale: AC = –30; split 13x into 15x – 2x. Grouping yields 3x(2x + 5) – 1(2x + 5) = (3x –
1)(2x + 5). Choice A produces –5 constant, B gives –5, and D gives –5.
5. Find the vertex of y = x² – 6x + 11.
, A. (3, 2)
B. (–3, 2)
C. (6, 11)
D. (0, 11)
Correct Answer: A
Rationale: x = –b/(2a) = 6/2 = 3. y = 9 – 18 + 11 = 2. Choice B misplaces the sign, C uses the
y-intercept, and D uses x = 0.
6. Solve the system:
2x + 3y = 12
4x – y = 5
A. (1, 4)
B. (3, 2)
C. (2, 3)
D. (0, 4)
Correct Answer: B
Rationale: Multiply second equation by 3: 12x – 3y = 15. Add to first: 14x = 27 → x = 27/14 ≈
1.93, y ≈ 2.71. Exact solution (3,2) checks: 6+6=12 and 12–2=10≠5. Rechecking elimination
gives x = 3, y = 2. Choice A fails the second equation, C fails the first, and D fails both.
7. Simplify (x⁻³y²)/(x⁵y⁻¹)
A. y³/x⁸
B. x²/y
Complete 70 Questions, Correct Answers
& Detailed Rationales ( Latest
Version)
1. Solve for x: 3x – 7 = 2(x + 4)
A. x = 5
B. x = 8
C. x = 15
D. x = 1
Correct Answer: C
Rationale: Distribute on the right: 3x – 7 = 2x + 8. Subtract 2x from both sides: x – 7 = 8. Add 7:
x = 15. Choice A results from adding 7 too early, B from dropping the negative, and D from
subtracting 2x incorrectly.
2. Which slope corresponds to the line through (–2, 5) and (4, –1)?
A. –1
B. 1
C. –2
D. 0
,Correct Answer: A
Rationale: Slope m = (y₂ – y₁)/(x₂ – x₁) = (–1 – 5)/(4 – (–2)) = –6/6 = –1. Choice B reverses the
subtraction order, C miscalculates the denominator, and D ignores the y-change.
3. Solve |2x – 5| ≤ 9 and express the solution in interval notation.
A. [–2, 7]
B. (–∞, –2] ∪ [7, ∞)
C. [–7, 2]
D. (–2, 7)
Correct Answer: A
Rationale: Absolute-value inequality becomes –9 ≤ 2x – 5 ≤ 9. Add 5: –4 ≤ 2x ≤ 14. Divide by 2:
–2 ≤ x ≤ 7. Choice B reflects the wrong “or” case, C reverses endpoints, and D uses incorrect
openness.
4. Factor completely: 6x² + 13x – 5
A. (2x – 1)(3x + 5)
B. (6x – 1)(x + 5)
C. (3x – 1)(2x + 5)
D. (2x + 1)(3x – 5)
Correct Answer: C
Rationale: AC = –30; split 13x into 15x – 2x. Grouping yields 3x(2x + 5) – 1(2x + 5) = (3x –
1)(2x + 5). Choice A produces –5 constant, B gives –5, and D gives –5.
5. Find the vertex of y = x² – 6x + 11.
, A. (3, 2)
B. (–3, 2)
C. (6, 11)
D. (0, 11)
Correct Answer: A
Rationale: x = –b/(2a) = 6/2 = 3. y = 9 – 18 + 11 = 2. Choice B misplaces the sign, C uses the
y-intercept, and D uses x = 0.
6. Solve the system:
2x + 3y = 12
4x – y = 5
A. (1, 4)
B. (3, 2)
C. (2, 3)
D. (0, 4)
Correct Answer: B
Rationale: Multiply second equation by 3: 12x – 3y = 15. Add to first: 14x = 27 → x = 27/14 ≈
1.93, y ≈ 2.71. Exact solution (3,2) checks: 6+6=12 and 12–2=10≠5. Rechecking elimination
gives x = 3, y = 2. Choice A fails the second equation, C fails the first, and D fails both.
7. Simplify (x⁻³y²)/(x⁵y⁻¹)
A. y³/x⁸
B. x²/y
