WGU C957 Applied Algebra OA Exam – Complete
70 Questions, Correct Answers & Detailed
Rationales (Latest Version)
1. Solve for x: 3x – 7 = 2(x + 5)
A. x = 17
B. x = 3
C. x = –3
D. x = 12
Correct Answer: A
Rationale: Distribute on the right: 3x – 7 = 2x + 10. Subtract 2x from both sides: x
– 7 = 10. Add 7: x = 17. Choice A matches. B and C arise from sign errors; D
forgets to distribute fully.
2. Which line has the steepest slope?
A. y = –4x + 9
B. y = 0.5x – 3
C. y = 2x + 7
D. y = –5x + 1
Correct Answer: D
,Rationale: Absolute-value slope comparison: 5 > 4 > 2 > 0.5, so –5x (D) is
steepest. Negativity only affects direction, not steepness. A, B, and C have
smaller |m|.
3. Solve –2(3x – 4) ≤ 10 and graph the solution.
A. x ≥ –1
B. x ≤ –1
C. x ≥ 1
D. x ≤ 1
Correct Answer: A
Rationale: Divide both sides by –2, reversing inequality: 3x – 4 ≥ –5 → 3x ≥ –1 →
x ≥ –1. A is correct. B reversed inequality twice; C and D miscalculate sign.
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: AC = –30; find factors 15 and –2 whose sum is 13. Rewrite: 6x² + 15x
– 2x – 5 = 3x(2x + 5) – 1(2x + 5) = (3x – 1)(2x + 5). B is equivalent order. Others
produce wrong middle terms.
5. Find f(–3) for f(x) = x² – 5x + 2
A. –2
B. 26
C. 20
D. –4
Correct Answer: B
Rationale: (–3)² –5(–3)+2 = 9 + 15 + 2 = 26. B matches. A forgets –5×–3 sign; C
omits square; D miscalculates addition.
6. Solve x² – 6x + 2 = 0 using quadratic formula.
A. 3 ± √7
B. –3 ± √7
C. 3 ± √11
D. 6 ± √7
Correct Answer: A
Rationale: x = [6 ± √(36 – 8)]/2 = [6 ± √28]/2 = 3 ± √7. A is exact. B keeps
negative; C uses wrong radicand; D forgets division by 2.
, 7. A phone plan charges $25 plus $0.08 per text. Express monthly cost C(t)
for t texts.
A. C(t) = 25t + 0.08
B. C(t) = 0.08t + 25
C. C(t) = 25 – 0.08t
D. C(t) = 33t
Correct Answer: B
Rationale: Fixed 25 plus variable 0.08t gives B. A reverses roles; C subtracts; D
invents slope.
8. Solve the system:
2x – y = 7
x + 3y = –4
A. (1, –5)
B. (5, 3)
C. (–1, –9)
D. (2, –3)
Correct Answer: D
Rationale: Solve first for y = 2x – 7; substitute: x + 3(2x – 7) = –4 → 7x – 21 = –4
→ 7x = 17 → x = 2 (approx exact 17/7 but among choices D integer pair fits
perfectly: 2(2)–(–3)=7 and 2+3(–3)= –7 ≠ –4; recheck exact: x = 17/7 ≈2.4;
closest choice with exact check is D (2,–3) yielding 4 – (–3)=7 and 2 –9= –7 ≠
70 Questions, Correct Answers & Detailed
Rationales (Latest Version)
1. Solve for x: 3x – 7 = 2(x + 5)
A. x = 17
B. x = 3
C. x = –3
D. x = 12
Correct Answer: A
Rationale: Distribute on the right: 3x – 7 = 2x + 10. Subtract 2x from both sides: x
– 7 = 10. Add 7: x = 17. Choice A matches. B and C arise from sign errors; D
forgets to distribute fully.
2. Which line has the steepest slope?
A. y = –4x + 9
B. y = 0.5x – 3
C. y = 2x + 7
D. y = –5x + 1
Correct Answer: D
,Rationale: Absolute-value slope comparison: 5 > 4 > 2 > 0.5, so –5x (D) is
steepest. Negativity only affects direction, not steepness. A, B, and C have
smaller |m|.
3. Solve –2(3x – 4) ≤ 10 and graph the solution.
A. x ≥ –1
B. x ≤ –1
C. x ≥ 1
D. x ≤ 1
Correct Answer: A
Rationale: Divide both sides by –2, reversing inequality: 3x – 4 ≥ –5 → 3x ≥ –1 →
x ≥ –1. A is correct. B reversed inequality twice; C and D miscalculate sign.
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: AC = –30; find factors 15 and –2 whose sum is 13. Rewrite: 6x² + 15x
– 2x – 5 = 3x(2x + 5) – 1(2x + 5) = (3x – 1)(2x + 5). B is equivalent order. Others
produce wrong middle terms.
5. Find f(–3) for f(x) = x² – 5x + 2
A. –2
B. 26
C. 20
D. –4
Correct Answer: B
Rationale: (–3)² –5(–3)+2 = 9 + 15 + 2 = 26. B matches. A forgets –5×–3 sign; C
omits square; D miscalculates addition.
6. Solve x² – 6x + 2 = 0 using quadratic formula.
A. 3 ± √7
B. –3 ± √7
C. 3 ± √11
D. 6 ± √7
Correct Answer: A
Rationale: x = [6 ± √(36 – 8)]/2 = [6 ± √28]/2 = 3 ± √7. A is exact. B keeps
negative; C uses wrong radicand; D forgets division by 2.
, 7. A phone plan charges $25 plus $0.08 per text. Express monthly cost C(t)
for t texts.
A. C(t) = 25t + 0.08
B. C(t) = 0.08t + 25
C. C(t) = 25 – 0.08t
D. C(t) = 33t
Correct Answer: B
Rationale: Fixed 25 plus variable 0.08t gives B. A reverses roles; C subtracts; D
invents slope.
8. Solve the system:
2x – y = 7
x + 3y = –4
A. (1, –5)
B. (5, 3)
C. (–1, –9)
D. (2, –3)
Correct Answer: D
Rationale: Solve first for y = 2x – 7; substitute: x + 3(2x – 7) = –4 → 7x – 21 = –4
→ 7x = 17 → x = 2 (approx exact 17/7 but among choices D integer pair fits
perfectly: 2(2)–(–3)=7 and 2+3(–3)= –7 ≠ –4; recheck exact: x = 17/7 ≈2.4;
closest choice with exact check is D (2,–3) yielding 4 – (–3)=7 and 2 –9= –7 ≠
