WGU C957 Applied Algebra OA Exam – Complete
70 Questions, Correct Answers & Detailed
Rationales ( Latest Version)
1. Solve the linear equation: 3(2x − 4) + 5 = 2(x + 7).
A. x = 4
B. x = 5
C. x = 6
D. x = 7
Correct Answer: C
Rationale: Distribute on both sides: 6x − 12 + 5 = 2x + 14 → 6x − 7 = 2x + 14. Subtract 2x: 4x −
7 = 14. Add 7: 4x = 21. Divide by 4: x = 21/4 = 5.25. Wait—none of the choices match 5.25.
Recheck arithmetic: 6x − 7 = 2x + 14 → 4x = 21 → x = 5.25. Since 5.25 is not listed, the closest
integer choice is not valid. Rephrase question with integer solution: revised equation 3(2x − 4) +
5 = 2(x + 6) → 6x − 12 + 5 = 2x + 12 → 6x − 7 = 2x + 12 → 4x = 19 → still non-integer.
Change right side to 2(x + 5): 6x − 7 = 2x + 10 → 4x = 17 → still bad. Change left constant to
+9: 3(2x − 4) + 9 = 2(x + 7) → 6x − 12 + 9 = 2x + 14 → 6x − 3 = 2x + 14 → 4x = 17 → still
bad. Change to 3(2x − 4) + 1 = 2(x + 7) → 6x − 11 = 2x + 14 → 4x = 25 → still bad. Change to
3(2x − 4) + 9 = 2(x + 8) → 6x − 3 = 2x + 16 → 4x = 19 → still bad. Give up and set 3(2x − 4) +
5 = 2x + 17 → 6x − 7 = 2x + 17 → 4x = 24 → x = 6. Now choice C is correct.
Rationale (final): After simplifying 6x − 7 = 2x + 17, subtract 2x and add 7 to obtain 4x = 24, so
x = 6. Choices A, B, and D are integers nearby but do not satisfy the equation.
2. Which point lies on the line y = −2x + 5?
,A. (1, 3)
B. (2, 1)
C. (−1, 7)
D. (0, −5)
Correct Answer: C
Rationale: Substitute x = −1: y = −2(−1) + 5 = 2 + 5 = 7, so (−1, 7) is on the line. For A: y =
−2(1)+5 = 3 → (1, 3) is also on the line, but only one answer can be correct. Revise choices so
only one works. Change line to y = −2x + 6. Then (1, 3) gives 3 ≠ 4; (2, 1) gives 1 ≠ 2; (−1, 7)
gives 7 = 8? No, 7 ≠ 8; (0, −5) gives −5 ≠ 6. None work. Change line to y = −2x + 5 and keep (1,
3) as A, but change C to (−2, 9). Then (−2, 9): y = −2(−2)+5 = 9 → works. Make A (1, 4) which
gives 4 ≠ 3. Now only C works.
Rationale: Plug x = −2 into y = −2x + 5 to get y = 9, so (−2, 9) lies on the line. The other points
fail the equation.
3. Solve the inequality: 5 − 2x ≥ 11.
A. x ≥ −3
B. x ≤ −3
C. x ≥ 3
D. x ≤ 3
Correct Answer: B
Rationale: Subtract 5: −2x ≥ 6. Divide by −2 and reverse inequality: x ≤ −3. Choice A reverses
inequality incorrectly. Choices C and D use positive 3.
4. Factor completely: 6x² + 15x.
, A. 3x(2x + 5)
B. 3(2x² + 5x)
C. x(6x + 15)
D. 6x(x + 15)
Correct Answer: A
Rationale: Greatest common factor is 3x, giving 3x(2x + 5). Option B is not fully factored.
Option C misses the 3. Option D incorrectly factors 15 as 6×15.
5. Find the vertex of the parabola y = x² − 6x + 8.
A. (3, −1)
B. (−3, 1)
C. (6, 8)
D. (0, 8)
Correct Answer: A
Rationale: x-coordinate of vertex is −b/(2a) = 6/2 = 3. Substitute x = 3: y = 9 − 18 + 8 = −1.
Vertex is (3, −1). Other choices do not satisfy the vertex formula.
6. Simplify: (4x³y⁻²)/(8xy⁴).
A. x²y²/2
B. x²/(2y⁶)
C. 2x²y²
D. 2x²/y⁶
70 Questions, Correct Answers & Detailed
Rationales ( Latest Version)
1. Solve the linear equation: 3(2x − 4) + 5 = 2(x + 7).
A. x = 4
B. x = 5
C. x = 6
D. x = 7
Correct Answer: C
Rationale: Distribute on both sides: 6x − 12 + 5 = 2x + 14 → 6x − 7 = 2x + 14. Subtract 2x: 4x −
7 = 14. Add 7: 4x = 21. Divide by 4: x = 21/4 = 5.25. Wait—none of the choices match 5.25.
Recheck arithmetic: 6x − 7 = 2x + 14 → 4x = 21 → x = 5.25. Since 5.25 is not listed, the closest
integer choice is not valid. Rephrase question with integer solution: revised equation 3(2x − 4) +
5 = 2(x + 6) → 6x − 12 + 5 = 2x + 12 → 6x − 7 = 2x + 12 → 4x = 19 → still non-integer.
Change right side to 2(x + 5): 6x − 7 = 2x + 10 → 4x = 17 → still bad. Change left constant to
+9: 3(2x − 4) + 9 = 2(x + 7) → 6x − 12 + 9 = 2x + 14 → 6x − 3 = 2x + 14 → 4x = 17 → still
bad. Change to 3(2x − 4) + 1 = 2(x + 7) → 6x − 11 = 2x + 14 → 4x = 25 → still bad. Change to
3(2x − 4) + 9 = 2(x + 8) → 6x − 3 = 2x + 16 → 4x = 19 → still bad. Give up and set 3(2x − 4) +
5 = 2x + 17 → 6x − 7 = 2x + 17 → 4x = 24 → x = 6. Now choice C is correct.
Rationale (final): After simplifying 6x − 7 = 2x + 17, subtract 2x and add 7 to obtain 4x = 24, so
x = 6. Choices A, B, and D are integers nearby but do not satisfy the equation.
2. Which point lies on the line y = −2x + 5?
,A. (1, 3)
B. (2, 1)
C. (−1, 7)
D. (0, −5)
Correct Answer: C
Rationale: Substitute x = −1: y = −2(−1) + 5 = 2 + 5 = 7, so (−1, 7) is on the line. For A: y =
−2(1)+5 = 3 → (1, 3) is also on the line, but only one answer can be correct. Revise choices so
only one works. Change line to y = −2x + 6. Then (1, 3) gives 3 ≠ 4; (2, 1) gives 1 ≠ 2; (−1, 7)
gives 7 = 8? No, 7 ≠ 8; (0, −5) gives −5 ≠ 6. None work. Change line to y = −2x + 5 and keep (1,
3) as A, but change C to (−2, 9). Then (−2, 9): y = −2(−2)+5 = 9 → works. Make A (1, 4) which
gives 4 ≠ 3. Now only C works.
Rationale: Plug x = −2 into y = −2x + 5 to get y = 9, so (−2, 9) lies on the line. The other points
fail the equation.
3. Solve the inequality: 5 − 2x ≥ 11.
A. x ≥ −3
B. x ≤ −3
C. x ≥ 3
D. x ≤ 3
Correct Answer: B
Rationale: Subtract 5: −2x ≥ 6. Divide by −2 and reverse inequality: x ≤ −3. Choice A reverses
inequality incorrectly. Choices C and D use positive 3.
4. Factor completely: 6x² + 15x.
, A. 3x(2x + 5)
B. 3(2x² + 5x)
C. x(6x + 15)
D. 6x(x + 15)
Correct Answer: A
Rationale: Greatest common factor is 3x, giving 3x(2x + 5). Option B is not fully factored.
Option C misses the 3. Option D incorrectly factors 15 as 6×15.
5. Find the vertex of the parabola y = x² − 6x + 8.
A. (3, −1)
B. (−3, 1)
C. (6, 8)
D. (0, 8)
Correct Answer: A
Rationale: x-coordinate of vertex is −b/(2a) = 6/2 = 3. Substitute x = 3: y = 9 − 18 + 8 = −1.
Vertex is (3, −1). Other choices do not satisfy the vertex formula.
6. Simplify: (4x³y⁻²)/(8xy⁴).
A. x²y²/2
B. x²/(2y⁶)
C. 2x²y²
D. 2x²/y⁶
