WGU C957 Applied Algebra OA Exam – Complete 70
Questions, Correct Answers & Detailed Rationales
( Latest Version)
1. Solve for x: 3x − 7 = 2x + 5
A. x = −12
B. x = 12
C. x = 2
D. x = −2
Correct Answer: B
Rationale: Subtract 2x from both sides to get x − 7 = 5. Add 7 to both sides to isolate x,
yielding x = 12. This is a one-step linear equation requiring inverse operations to isolate
the variable. The other choices result from sign errors or incorrect combining of like
terms.
2. Which line has a slope of −4 and y-intercept 9?
A. y = 9x − 4
B. y = −4x + 9
C. y = 4x + 9
D. y = −4x − 9
Correct Answer: B
Rationale: Slope-intercept form is y = mx + b where m is slope and b is y-intercept. Only
choice B matches m = −4 and b = 9. Choice A reverses slope and intercept, while C and
D have incorrect signs.
3. Solve the inequality 5 − 2x ≥ 11. Write the solution in interval notation.
A. (−∞, −3]
B. [−3, ∞)
, C. (−∞, 3]
D. [3, ∞)
Correct Answer: A
Rationale: Subtract 5 from both sides: −2x ≥ 6. Divide by −2 and reverse the inequality
sign: x ≤ −3. Interval notation uses parenthesis for infinity and bracket for included
endpoint, giving (−∞, −3]. Choices B and D show reversed inequality directions, while C
uses the wrong boundary.
4. Factor completely: 6x² + 15x
A. 3x(2x + 5)
B. 3x(2x − 5)
C. 6x(x + 5)
D. x(6x + 15)
Correct Answer: A
Rationale: The greatest common factor is 3x. Factoring 3x from each term yields 3x(2x +
5). Choice B keeps an incorrect sign, C does not factor out the largest GCF, and D leaves
a factorable expression inside parentheses.
5. Find f(−2) for the function f(x) = x² − 5x + 3
A. −11
B. 17
C. 7
D. −7
Correct Answer: B
Rationale: Substitute −2 into the quadratic: (−2)² − 5(−2) + 3 = 4 + 10 + 3 = 17. Common
errors include sign mistakes in the middle term, leading to the other choices.
6. Solve the system:
2x + y = 7
, x − y = −1
A. (2, 3)
B. (3, 1)
C. (1, 5)
D. (4, −1)
Correct Answer: A
Rationale: Add the two equations to eliminate y: 3x = 6 ⇒ x = 2. Substitute x = 2 into
either equation to find y = 3. Choices B and C satisfy only one equation, while D satisfies
neither.
7. Simplify (2x³)²
A. 2x⁵
B. 4x⁵
C. 4x⁶
D. 2x⁶
Correct Answer: C
Rationale: Power-of-a-product rule: (2x³)² = 2²(x³)² = 4x⁶. Choices A and B add
exponents instead of multiplying them, while D forgets to square the coefficient.
8. A rectangle’s length is 5 cm more than its width. If the perimeter is 38 cm, find the
width.
A. 7 cm
B. 8 cm
C. 9 cm
D. 12 cm
Correct Answer: A
Rationale: Let width = w, length = w + 5. Perimeter formula 2(w + w + 5) = 38 simplifies
to 4w + 10 = 38, so w = 7 cm. Other choices misinterpret the relationship between length
and width or make arithmetic errors.
Questions, Correct Answers & Detailed Rationales
( Latest Version)
1. Solve for x: 3x − 7 = 2x + 5
A. x = −12
B. x = 12
C. x = 2
D. x = −2
Correct Answer: B
Rationale: Subtract 2x from both sides to get x − 7 = 5. Add 7 to both sides to isolate x,
yielding x = 12. This is a one-step linear equation requiring inverse operations to isolate
the variable. The other choices result from sign errors or incorrect combining of like
terms.
2. Which line has a slope of −4 and y-intercept 9?
A. y = 9x − 4
B. y = −4x + 9
C. y = 4x + 9
D. y = −4x − 9
Correct Answer: B
Rationale: Slope-intercept form is y = mx + b where m is slope and b is y-intercept. Only
choice B matches m = −4 and b = 9. Choice A reverses slope and intercept, while C and
D have incorrect signs.
3. Solve the inequality 5 − 2x ≥ 11. Write the solution in interval notation.
A. (−∞, −3]
B. [−3, ∞)
, C. (−∞, 3]
D. [3, ∞)
Correct Answer: A
Rationale: Subtract 5 from both sides: −2x ≥ 6. Divide by −2 and reverse the inequality
sign: x ≤ −3. Interval notation uses parenthesis for infinity and bracket for included
endpoint, giving (−∞, −3]. Choices B and D show reversed inequality directions, while C
uses the wrong boundary.
4. Factor completely: 6x² + 15x
A. 3x(2x + 5)
B. 3x(2x − 5)
C. 6x(x + 5)
D. x(6x + 15)
Correct Answer: A
Rationale: The greatest common factor is 3x. Factoring 3x from each term yields 3x(2x +
5). Choice B keeps an incorrect sign, C does not factor out the largest GCF, and D leaves
a factorable expression inside parentheses.
5. Find f(−2) for the function f(x) = x² − 5x + 3
A. −11
B. 17
C. 7
D. −7
Correct Answer: B
Rationale: Substitute −2 into the quadratic: (−2)² − 5(−2) + 3 = 4 + 10 + 3 = 17. Common
errors include sign mistakes in the middle term, leading to the other choices.
6. Solve the system:
2x + y = 7
, x − y = −1
A. (2, 3)
B. (3, 1)
C. (1, 5)
D. (4, −1)
Correct Answer: A
Rationale: Add the two equations to eliminate y: 3x = 6 ⇒ x = 2. Substitute x = 2 into
either equation to find y = 3. Choices B and C satisfy only one equation, while D satisfies
neither.
7. Simplify (2x³)²
A. 2x⁵
B. 4x⁵
C. 4x⁶
D. 2x⁶
Correct Answer: C
Rationale: Power-of-a-product rule: (2x³)² = 2²(x³)² = 4x⁶. Choices A and B add
exponents instead of multiplying them, while D forgets to square the coefficient.
8. A rectangle’s length is 5 cm more than its width. If the perimeter is 38 cm, find the
width.
A. 7 cm
B. 8 cm
C. 9 cm
D. 12 cm
Correct Answer: A
Rationale: Let width = w, length = w + 5. Perimeter formula 2(w + w + 5) = 38 simplifies
to 4w + 10 = 38, so w = 7 cm. Other choices misinterpret the relationship between length
and width or make arithmetic errors.
