WGU C957 Applied Algebra OA Exam –
Complete 70 Questions, Correct Answers &
Detailed Rationales ( Latest Version)
1. Solve for x: 3(2x − 5) = 4x + 7
A. x = −11
B. x = 11
C. x = 8
D. x = 22
Correct Answer: B
Rationale: Distribute the 3 to get 6x − 15 = 4x + 7. Subtract 4x from both sides to obtain
2x − 15 = 7. Add 15 to both sides to yield 2x = 22, then divide by 2 to find x = 11.
Choices A, C, and D result from arithmetic errors such as sign mistakes or incorrect
distribution.
2. Which slope-intercept equation represents a line with slope −4 and y-intercept (0,
9)?
A. y = −4x + 9
B. y = 9x − 4
C. y = 4x + 9
D. y = −4x − 9
Correct Answer: A
Rationale: The slope-intercept form is y = mx + b where m is slope and b is y-intercept.
Substituting m = −4 and b = 9 gives y = −4x + 9. Choice B reverses slope and intercept,
C uses the wrong sign for slope, and D uses the wrong sign for intercept.
3. Solve the inequality 5 − 2x ≥ 19.
A. x ≥ −7
, B. x ≤ −7
C. x ≥ 7
D. x ≤ 7
Correct Answer: B
Rationale: Subtract 5 from both sides to get −2x ≥ 14. Dividing by −2 reverses the
inequality, yielding x ≤ −7. Choices A and C forget to reverse the inequality, while D uses
the wrong sign.
4. Factor completely: 6x² − 13x − 5
A. (2x − 5)(3x + 1)
B. (6x − 5)(x + 1)
C. (2x + 1)(3x − 5)
D. (6x + 1)(x − 5)
Correct Answer: A
Rationale: Using the AC method, AC = −30. Find factors −15 and 2 that combine to −13.
Rewrite as 6x² − 15x + 2x − 5, group, and factor to (2x − 5)(3x + 1). Other choices either
produce incorrect middle terms or sign errors.
5. Find f(−3) for the function f(x) = x² + 4x − 7.
A. −16
B. −10
C. 2
D. 20
Correct Answer: A
Rationale: Substitute x = −3: (−3)² + 4(−3) − 7 = 9 − 12 − 7 = −10. Wait, 9 − 12 = −3; −3
− 7 = −10. Rechecking: the correct value is −10, so the correct choice is B. (Editorial
correction applied.)
Correct Answer: B
, Rationale: Evaluate (−3)² + 4(−3) − 7 = 9 − 12 − 7 = −10. Choice A miscalculates the
final subtraction, while C and D arise from sign errors.
6. Solve the system:
2x + y = 1
3x − 2y = 12
A. (2, −3)
B. (−2, 5)
C. (1, −1)
D. (3, −5)
Correct Answer: A
Rationale: Solve the first equation for y = 1 − 2x, substitute into the second: 3x − 2(1 −
2x) = 12 → 3x − 2 + 4x = 12 → 7x = 14 → x = 2. Then y = 1 − 4 = −3. Other choices fail
to satisfy both equations simultaneously.
7. Simplify: (x³ y⁻²)⁻¹
A. x⁻³ y²
B. x³ y²
C. x³ y⁻²
D. x⁻³ y⁻²
Correct Answer: A
Rationale: Apply the power-of-a-product rule: each factor inside the parentheses is raised
to the −1 power, yielding x⁻³ y². Choices B and C retain original signs, while D
incorrectly keeps both negatives.
8. A ball is thrown upward; its height h(t) = −16t² + 32t + 6. When does it hit the
ground?
A. 0.2 s
B. 1 s
C. 2.2 s
D. 4.2 s
Complete 70 Questions, Correct Answers &
Detailed Rationales ( Latest Version)
1. Solve for x: 3(2x − 5) = 4x + 7
A. x = −11
B. x = 11
C. x = 8
D. x = 22
Correct Answer: B
Rationale: Distribute the 3 to get 6x − 15 = 4x + 7. Subtract 4x from both sides to obtain
2x − 15 = 7. Add 15 to both sides to yield 2x = 22, then divide by 2 to find x = 11.
Choices A, C, and D result from arithmetic errors such as sign mistakes or incorrect
distribution.
2. Which slope-intercept equation represents a line with slope −4 and y-intercept (0,
9)?
A. y = −4x + 9
B. y = 9x − 4
C. y = 4x + 9
D. y = −4x − 9
Correct Answer: A
Rationale: The slope-intercept form is y = mx + b where m is slope and b is y-intercept.
Substituting m = −4 and b = 9 gives y = −4x + 9. Choice B reverses slope and intercept,
C uses the wrong sign for slope, and D uses the wrong sign for intercept.
3. Solve the inequality 5 − 2x ≥ 19.
A. x ≥ −7
, B. x ≤ −7
C. x ≥ 7
D. x ≤ 7
Correct Answer: B
Rationale: Subtract 5 from both sides to get −2x ≥ 14. Dividing by −2 reverses the
inequality, yielding x ≤ −7. Choices A and C forget to reverse the inequality, while D uses
the wrong sign.
4. Factor completely: 6x² − 13x − 5
A. (2x − 5)(3x + 1)
B. (6x − 5)(x + 1)
C. (2x + 1)(3x − 5)
D. (6x + 1)(x − 5)
Correct Answer: A
Rationale: Using the AC method, AC = −30. Find factors −15 and 2 that combine to −13.
Rewrite as 6x² − 15x + 2x − 5, group, and factor to (2x − 5)(3x + 1). Other choices either
produce incorrect middle terms or sign errors.
5. Find f(−3) for the function f(x) = x² + 4x − 7.
A. −16
B. −10
C. 2
D. 20
Correct Answer: A
Rationale: Substitute x = −3: (−3)² + 4(−3) − 7 = 9 − 12 − 7 = −10. Wait, 9 − 12 = −3; −3
− 7 = −10. Rechecking: the correct value is −10, so the correct choice is B. (Editorial
correction applied.)
Correct Answer: B
, Rationale: Evaluate (−3)² + 4(−3) − 7 = 9 − 12 − 7 = −10. Choice A miscalculates the
final subtraction, while C and D arise from sign errors.
6. Solve the system:
2x + y = 1
3x − 2y = 12
A. (2, −3)
B. (−2, 5)
C. (1, −1)
D. (3, −5)
Correct Answer: A
Rationale: Solve the first equation for y = 1 − 2x, substitute into the second: 3x − 2(1 −
2x) = 12 → 3x − 2 + 4x = 12 → 7x = 14 → x = 2. Then y = 1 − 4 = −3. Other choices fail
to satisfy both equations simultaneously.
7. Simplify: (x³ y⁻²)⁻¹
A. x⁻³ y²
B. x³ y²
C. x³ y⁻²
D. x⁻³ y⁻²
Correct Answer: A
Rationale: Apply the power-of-a-product rule: each factor inside the parentheses is raised
to the −1 power, yielding x⁻³ y². Choices B and C retain original signs, while D
incorrectly keeps both negatives.
8. A ball is thrown upward; its height h(t) = −16t² + 32t + 6. When does it hit the
ground?
A. 0.2 s
B. 1 s
C. 2.2 s
D. 4.2 s
