WGU C957 Applied Algebra OA Exam – Complete
70 Questions, Correct Answers & Detailed
Rationales ( Latest Version)
1. Solve for x: 3(2x – 5) = 2x + 7
A. x = –4
B. x = –1
C. x = 5.5
D. x = 11
Correct Answer: C
Rationale: Distribute the 3 to get 6x – 15 = 2x + 7. Subtract 2x from both sides: 4x – 15 =
7. Add 15: 4x = 22. Divide by 4: x = 5.5. Choice C is the only value that satisfies the
equation when substituted back.
2. Which point lies on the line y = –4x + 9?
A. (2, 1)
B. (–1, 5)
C. (0, –9)
D. (3, –3)
Correct Answer: A
Rationale: Substitute x = 2 into the equation: y = –4(2) + 9 = –8 + 9 = 1. Because the
y-value of point (2, 1) matches the computed value, the point lies on the line. The other
choices fail the substitution test.
3. Solve the inequality 5 – 2x ≤ 11 and graph the solution on a number line.
A. x ≥ –3 (closed circle, shade right)
B. x ≤ –3 (closed circle, shade left)
, C. x ≥ 3 (closed circle, shade right)
D. x ≤ 3 (closed circle, shade left)
Correct Answer: A
Rationale: Subtract 5 from both sides: –2x ≤ 6. Divide by –2, reversing the inequality: x ≥
–3. A closed circle at –3 with shading to the right represents all numbers greater than or
equal to –3.
4. Multiply (3x – 4)(2x + 5) and select the correct trinomial.
A. 6x² – 7x – 20
B. 6x² + x – 20
C. 5x² + 7x – 20
D. 6x² + 23x – 20
Correct Answer: B
Rationale: Use FOIL: 3x·2x = 6x², 3x·5 = 15x, –4·2x = –8x, –4·5 = –20. Combine like
terms: 6x² + 7x – 20. Choice B matches this result.
5. Factor completely: 4x² – 36
A. 4(x – 3)(x + 3)
B. 4(x – 3)²
C. (2x – 6)(2x + 6)
D. 2(x – 3)(x + 3)
Correct Answer: A
Rationale: First factor out the GCF of 4: 4(x² – 9). Recognize x² – 9 as a difference of
squares: (x – 3)(x + 3). Thus 4(x – 3)(x + 3) is the complete factorization.
6. Given f(x) = x² – 5x + 8, find f(–2).
A. –6
B. 2
C. 22
D. 18
, Correct Answer: C
Rationale: Substitute –2 for x: (–2)² –5(–2)+8 = 4 + 10 + 8 = 22. None of the other
choices produce 22, so C is correct.
7. Solve x² – 6x + 8 = 0 by factoring.
A. x = –4, –2
B. x = 2, 4
C. x = –2, 4
D. x = 1, 8
Correct Answer: B
Rationale: Factor to (x – 2)(x – 4) = 0. Setting each factor equal to zero gives x = 2 and x
= 4. Substituting either value satisfies the original equation.
8. Solve the system:
2x + y = 10
x – y = 2
A. (4, 2)
B. (3, 4)
C. (2, 6)
D. (6, –2)
Correct Answer: A
Rationale: Add the two equations to eliminate y: 3x = 12 → x = 4. Substitute x = 4 into
the first equation: 8 + y = 10 → y = 2. The ordered pair (4, 2) satisfies both equations.
9. Simplify √(50x⁵) assuming x > 0.
A. 5x²√(2x)
B. 10x√(5x)
C. 2x√(25x)
D. 25x²√(2x)
Correct Answer: A
70 Questions, Correct Answers & Detailed
Rationales ( Latest Version)
1. Solve for x: 3(2x – 5) = 2x + 7
A. x = –4
B. x = –1
C. x = 5.5
D. x = 11
Correct Answer: C
Rationale: Distribute the 3 to get 6x – 15 = 2x + 7. Subtract 2x from both sides: 4x – 15 =
7. Add 15: 4x = 22. Divide by 4: x = 5.5. Choice C is the only value that satisfies the
equation when substituted back.
2. Which point lies on the line y = –4x + 9?
A. (2, 1)
B. (–1, 5)
C. (0, –9)
D. (3, –3)
Correct Answer: A
Rationale: Substitute x = 2 into the equation: y = –4(2) + 9 = –8 + 9 = 1. Because the
y-value of point (2, 1) matches the computed value, the point lies on the line. The other
choices fail the substitution test.
3. Solve the inequality 5 – 2x ≤ 11 and graph the solution on a number line.
A. x ≥ –3 (closed circle, shade right)
B. x ≤ –3 (closed circle, shade left)
, C. x ≥ 3 (closed circle, shade right)
D. x ≤ 3 (closed circle, shade left)
Correct Answer: A
Rationale: Subtract 5 from both sides: –2x ≤ 6. Divide by –2, reversing the inequality: x ≥
–3. A closed circle at –3 with shading to the right represents all numbers greater than or
equal to –3.
4. Multiply (3x – 4)(2x + 5) and select the correct trinomial.
A. 6x² – 7x – 20
B. 6x² + x – 20
C. 5x² + 7x – 20
D. 6x² + 23x – 20
Correct Answer: B
Rationale: Use FOIL: 3x·2x = 6x², 3x·5 = 15x, –4·2x = –8x, –4·5 = –20. Combine like
terms: 6x² + 7x – 20. Choice B matches this result.
5. Factor completely: 4x² – 36
A. 4(x – 3)(x + 3)
B. 4(x – 3)²
C. (2x – 6)(2x + 6)
D. 2(x – 3)(x + 3)
Correct Answer: A
Rationale: First factor out the GCF of 4: 4(x² – 9). Recognize x² – 9 as a difference of
squares: (x – 3)(x + 3). Thus 4(x – 3)(x + 3) is the complete factorization.
6. Given f(x) = x² – 5x + 8, find f(–2).
A. –6
B. 2
C. 22
D. 18
, Correct Answer: C
Rationale: Substitute –2 for x: (–2)² –5(–2)+8 = 4 + 10 + 8 = 22. None of the other
choices produce 22, so C is correct.
7. Solve x² – 6x + 8 = 0 by factoring.
A. x = –4, –2
B. x = 2, 4
C. x = –2, 4
D. x = 1, 8
Correct Answer: B
Rationale: Factor to (x – 2)(x – 4) = 0. Setting each factor equal to zero gives x = 2 and x
= 4. Substituting either value satisfies the original equation.
8. Solve the system:
2x + y = 10
x – y = 2
A. (4, 2)
B. (3, 4)
C. (2, 6)
D. (6, –2)
Correct Answer: A
Rationale: Add the two equations to eliminate y: 3x = 12 → x = 4. Substitute x = 4 into
the first equation: 8 + y = 10 → y = 2. The ordered pair (4, 2) satisfies both equations.
9. Simplify √(50x⁵) assuming x > 0.
A. 5x²√(2x)
B. 10x√(5x)
C. 2x√(25x)
D. 25x²√(2x)
Correct Answer: A
