WGU C957 Applied Algebra OA Exam – Complete
70 Questions, Correct Answers & Detailed
Rationales ( Latest Version)
1. Solve for x: 3x – 7 = 2x + 5
A. –12
B. –2
C. 12
D. 2
Correct Answer: C
Rationale: Subtract 2x from both sides to get x – 7 = 5. Add 7 to both sides to isolate x,
yielding x = 12. Choices A and B incorrectly handle signs, while D results from adding 7
to the right side only.
2. Which line has a steeper slope: y = 4x – 9 or y = –5x + 2?
A. y = 4x – 9
B. y = –5x + 2
C. They are equally steep
D. Cannot be determined
Correct Answer: B
Rationale: Steepness is captured by the absolute value of the slope. |–5| = 5 exceeds |4|, so
y = –5x + 2 is steeper. Choice A ignores absolute value, C is false, and D is unnecessary
because slopes are given explicitly.
3. Solve the inequality 2(3 – x) ≤ 8 and express the solution in interval notation.
A. [–1, ∞)
B. (–∞, –1]
, C. (–∞, 1]
D. [1, ∞)
Correct Answer: A
Rationale: Distribute to get 6 – 2x ≤ 8. Subtract 6: –2x ≤ 2. Divide by –2 (reverse
inequality): x ≥ –1, i.e., [–1, ∞). B reverses the sign incorrectly, C uses 1 instead of –1,
and D uses the wrong bound.
4. Factor completely: 6x² + 13x – 5
A. (2x – 1)(3x + 5)
B. (2x + 5)(3x – 1)
C. (6x – 1)(x + 5)
D. (3x + 1)(2x – 5)
Correct Answer: B
Rationale: Using grouping or trial, 6x² + 13x – 5 = (2x + 5)(3x – 1). FOIL returns the
original trinomial. A produces –13x, C gives 29x, and D yields –13x, each failing the
middle term.
5. Find f(–3) for f(x) = x² – 5x + 2
A. –22
B. 26
C. –4
D. 14
Correct Answer: B
Rationale: Substitute –3: (–3)² – 5(–3) + 2 = 9 + 15 + 2 = 26. A miscalculates signs, C
forgets the squared term, and D drops the double-negative.
6. Solve x² – 8x + 12 = 0 by factoring.
A. x = 2, 6
B. x = –2, –6
, C. x = 4, 3
D. x = –4, –3
Correct Answer: A
Rationale: Factors as (x – 2)(x – 6) = 0 ⇒ x = 2 or 6. B reverses signs, C uses factors of
12 that do not sum to –8, and D also reverses signs.
7. Simplify (2x³y⁻²)³
A. 6x⁹y⁻⁵
B. 8x⁶y⁻⁶
C. 8x⁹y⁻⁶
D. 6x⁶y⁻⁵
Correct Answer: C
Rationale: Power of product equals product of powers: 2³ = 8, (x³)³ = x⁹, (y⁻²)³ = y⁻⁶. A
and D miscalculate coefficients, B errs on the x-exponent.
8. A rectangle’s length is 4 cm more than its width. If the perimeter is 48 cm, find the
width.
A. 10 cm
B. 12 cm
C. 14 cm
D. 8 cm
Correct Answer: A
Rationale: Let width = w, length = w + 4. Perimeter 2(w + w + 4) = 48 ⇒ 4w + 8 = 48 ⇒
w = 10. B confuses with half-perimeter, C uses length, and D ignores the +4.
9. Which system has infinitely many solutions?
A. y = 3x + 2; y = –3x + 2
B. 2x – y = 5; 4x – 2y = 10
C. x + y = 1; x + y = 2
D. y = 4x; y = 4x + 1
70 Questions, Correct Answers & Detailed
Rationales ( Latest Version)
1. Solve for x: 3x – 7 = 2x + 5
A. –12
B. –2
C. 12
D. 2
Correct Answer: C
Rationale: Subtract 2x from both sides to get x – 7 = 5. Add 7 to both sides to isolate x,
yielding x = 12. Choices A and B incorrectly handle signs, while D results from adding 7
to the right side only.
2. Which line has a steeper slope: y = 4x – 9 or y = –5x + 2?
A. y = 4x – 9
B. y = –5x + 2
C. They are equally steep
D. Cannot be determined
Correct Answer: B
Rationale: Steepness is captured by the absolute value of the slope. |–5| = 5 exceeds |4|, so
y = –5x + 2 is steeper. Choice A ignores absolute value, C is false, and D is unnecessary
because slopes are given explicitly.
3. Solve the inequality 2(3 – x) ≤ 8 and express the solution in interval notation.
A. [–1, ∞)
B. (–∞, –1]
, C. (–∞, 1]
D. [1, ∞)
Correct Answer: A
Rationale: Distribute to get 6 – 2x ≤ 8. Subtract 6: –2x ≤ 2. Divide by –2 (reverse
inequality): x ≥ –1, i.e., [–1, ∞). B reverses the sign incorrectly, C uses 1 instead of –1,
and D uses the wrong bound.
4. Factor completely: 6x² + 13x – 5
A. (2x – 1)(3x + 5)
B. (2x + 5)(3x – 1)
C. (6x – 1)(x + 5)
D. (3x + 1)(2x – 5)
Correct Answer: B
Rationale: Using grouping or trial, 6x² + 13x – 5 = (2x + 5)(3x – 1). FOIL returns the
original trinomial. A produces –13x, C gives 29x, and D yields –13x, each failing the
middle term.
5. Find f(–3) for f(x) = x² – 5x + 2
A. –22
B. 26
C. –4
D. 14
Correct Answer: B
Rationale: Substitute –3: (–3)² – 5(–3) + 2 = 9 + 15 + 2 = 26. A miscalculates signs, C
forgets the squared term, and D drops the double-negative.
6. Solve x² – 8x + 12 = 0 by factoring.
A. x = 2, 6
B. x = –2, –6
, C. x = 4, 3
D. x = –4, –3
Correct Answer: A
Rationale: Factors as (x – 2)(x – 6) = 0 ⇒ x = 2 or 6. B reverses signs, C uses factors of
12 that do not sum to –8, and D also reverses signs.
7. Simplify (2x³y⁻²)³
A. 6x⁹y⁻⁵
B. 8x⁶y⁻⁶
C. 8x⁹y⁻⁶
D. 6x⁶y⁻⁵
Correct Answer: C
Rationale: Power of product equals product of powers: 2³ = 8, (x³)³ = x⁹, (y⁻²)³ = y⁻⁶. A
and D miscalculate coefficients, B errs on the x-exponent.
8. A rectangle’s length is 4 cm more than its width. If the perimeter is 48 cm, find the
width.
A. 10 cm
B. 12 cm
C. 14 cm
D. 8 cm
Correct Answer: A
Rationale: Let width = w, length = w + 4. Perimeter 2(w + w + 4) = 48 ⇒ 4w + 8 = 48 ⇒
w = 10. B confuses with half-perimeter, C uses length, and D ignores the +4.
9. Which system has infinitely many solutions?
A. y = 3x + 2; y = –3x + 2
B. 2x – y = 5; 4x – 2y = 10
C. x + y = 1; x + y = 2
D. y = 4x; y = 4x + 1
