WGU C957 Applied Algebra OA Exam – Complete 70
Questions, Correct Answers & Detailed Rationales
( Latest Version)
1. Solve for x: 4(2x – 3) = 5x + 9
A. 1
B. 3
C. 7
D. 9
Correct Answer: C
Rationale: Distribute the 4 to get 8x – 12 = 5x + 9. Subtract 5x from both sides: 3x – 12 =
9. Add 12 to both sides: 3x = 21. Divide by 3: x = 7. Choices A, B, and D result from
arithmetic slips such as forgetting to distribute the 4 or mishandling the subtraction of 12.
2. Which line has the steepest slope?
A. y = –3x + 4
B. y = 0.5x – 7
C. y = 2x + 1
D. y = –5x + 9
Correct Answer: D
Rationale: The slope (coefficient of x) in D is –5, whose absolute value 5 is greater than
the absolute values of the slopes in A (3), B (0.5), and C (2). A larger absolute slope
means a steeper line, so D is steepest.
, 3. Solve the inequality –3x + 7 ≤ 19 and graph the solution on a number line.
A. x ≥ –4
B. x ≤ –4
C. x ≥ 4
D. x ≤ 4
Correct Answer: A
Rationale: Subtract 7 from both sides: –3x ≤ 12. Divide by –3 and reverse the inequality
sign: x ≥ –4. Choices B and D retain the wrong sign after division by a negative, while C
reverses the inequality incorrectly.
4. Factor completely: 6x² – 5x – 4
A. (3x – 4)(2x + 1)
B. (6x + 1)(x – 4)
C. (3x + 4)(2x – 1)
D. (6x – 1)(x + 4)
Correct Answer: A
Rationale: Multiply the choices to verify. (3x – 4)(2x + 1) = 6x² + 3x – 8x – 4 = 6x² – 5x
– 4, matching the original. Other products either give wrong middle terms or wrong
constants.
5. Find f(–2) for the function f(x) = x³ – 3x² + 4x – 1
A. –29
B. –21
C. –13
D. –9
Correct Answer: B
,Rationale: Substitute –2: (–2)³ – 3(–2)² + 4(–2) – 1 = –8 – 12 – 8 – 1 = –29.
Wait—recheck arithmetic: –8 –12 = –20; –20 –8 = –28; –28 –1 = –29. The provided
correct choice was B (–21) but actual value is –29, so the choices need to align. Reprint
choices:
A. –29
B. –25
C. –21
D. –17
Correct Answer: A
Rationale: As calculated, f(–2) = –29. Choices B, C, and D stem from sign errors when
squaring –2 or distributing the 4.
6. Solve the system:
2x + 3y = 12
4x – y = 5
A. (1.5, 3)
B. (2, 3)
C. (3, 2)
D. (3, 3)
Correct Answer: C
, Rationale: Solve the second equation for y: y = 4x – 5. Substitute into the first: 2x + 3(4x
– 5) = 12 → 2x + 12x – 15 = 12 → 14x = 27 → x = 27/14 ≈ 1.928—not matching
choices. Re-cast with elimination: multiply second equation by 3: 12x – 3y = 15. Add to
first: 14x = 27 → same. Re-write system with integer-friendly numbers:
Revised system for exam:
2x + 3y = 12
4x – y = 5
Multiply second by 3: 12x – 3y = 15. Add: 14x = 27 → x = 27/14. To keep integer
solution, change constants:
New system:
2x + 3y = 12
4x – y = 10
Multiply second by 3: 12x – 3y = 30. Add: 14x = 42 → x = 3. Then y = 4(3) – 10 = 2.
Point (3, 2) is choice C. Other choices satisfy only one equation.
7. Simplify: (2x²y⁻³)⁻²
A. x⁻⁴y⁶/4
B. 4x⁻⁴y⁶
C. x⁴y⁶/4
D. 4x⁴y⁻⁶
Questions, Correct Answers & Detailed Rationales
( Latest Version)
1. Solve for x: 4(2x – 3) = 5x + 9
A. 1
B. 3
C. 7
D. 9
Correct Answer: C
Rationale: Distribute the 4 to get 8x – 12 = 5x + 9. Subtract 5x from both sides: 3x – 12 =
9. Add 12 to both sides: 3x = 21. Divide by 3: x = 7. Choices A, B, and D result from
arithmetic slips such as forgetting to distribute the 4 or mishandling the subtraction of 12.
2. Which line has the steepest slope?
A. y = –3x + 4
B. y = 0.5x – 7
C. y = 2x + 1
D. y = –5x + 9
Correct Answer: D
Rationale: The slope (coefficient of x) in D is –5, whose absolute value 5 is greater than
the absolute values of the slopes in A (3), B (0.5), and C (2). A larger absolute slope
means a steeper line, so D is steepest.
, 3. Solve the inequality –3x + 7 ≤ 19 and graph the solution on a number line.
A. x ≥ –4
B. x ≤ –4
C. x ≥ 4
D. x ≤ 4
Correct Answer: A
Rationale: Subtract 7 from both sides: –3x ≤ 12. Divide by –3 and reverse the inequality
sign: x ≥ –4. Choices B and D retain the wrong sign after division by a negative, while C
reverses the inequality incorrectly.
4. Factor completely: 6x² – 5x – 4
A. (3x – 4)(2x + 1)
B. (6x + 1)(x – 4)
C. (3x + 4)(2x – 1)
D. (6x – 1)(x + 4)
Correct Answer: A
Rationale: Multiply the choices to verify. (3x – 4)(2x + 1) = 6x² + 3x – 8x – 4 = 6x² – 5x
– 4, matching the original. Other products either give wrong middle terms or wrong
constants.
5. Find f(–2) for the function f(x) = x³ – 3x² + 4x – 1
A. –29
B. –21
C. –13
D. –9
Correct Answer: B
,Rationale: Substitute –2: (–2)³ – 3(–2)² + 4(–2) – 1 = –8 – 12 – 8 – 1 = –29.
Wait—recheck arithmetic: –8 –12 = –20; –20 –8 = –28; –28 –1 = –29. The provided
correct choice was B (–21) but actual value is –29, so the choices need to align. Reprint
choices:
A. –29
B. –25
C. –21
D. –17
Correct Answer: A
Rationale: As calculated, f(–2) = –29. Choices B, C, and D stem from sign errors when
squaring –2 or distributing the 4.
6. Solve the system:
2x + 3y = 12
4x – y = 5
A. (1.5, 3)
B. (2, 3)
C. (3, 2)
D. (3, 3)
Correct Answer: C
, Rationale: Solve the second equation for y: y = 4x – 5. Substitute into the first: 2x + 3(4x
– 5) = 12 → 2x + 12x – 15 = 12 → 14x = 27 → x = 27/14 ≈ 1.928—not matching
choices. Re-cast with elimination: multiply second equation by 3: 12x – 3y = 15. Add to
first: 14x = 27 → same. Re-write system with integer-friendly numbers:
Revised system for exam:
2x + 3y = 12
4x – y = 5
Multiply second by 3: 12x – 3y = 15. Add: 14x = 27 → x = 27/14. To keep integer
solution, change constants:
New system:
2x + 3y = 12
4x – y = 10
Multiply second by 3: 12x – 3y = 30. Add: 14x = 42 → x = 3. Then y = 4(3) – 10 = 2.
Point (3, 2) is choice C. Other choices satisfy only one equation.
7. Simplify: (2x²y⁻³)⁻²
A. x⁻⁴y⁶/4
B. 4x⁻⁴y⁶
C. x⁴y⁶/4
D. 4x⁴y⁻⁶
