WGU C957 Applied Algebra OA Exam
– Complete 70 Questions, Correct
Answers & Detailed Rationales (2025 /
2026 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: To solve this linear equation, we need to isolate x on one side. First,
subtract 2x from both sides: 3x - 2x - 7 = 5, which simplifies to x - 7 = 5. Then add
7 to both sides: x = 12. We can verify this by substituting x = 12 back into the
original equation: 3(12) - 7 = 36 - 7 = 29 and 2(12) + 5 = 24 + 5 = 29. Since both
sides equal 29, our solution is correct.
2. Find the slope of the line passing through points (2, 5) and (-3, 1)
A. 4/5
B. -4/5
C. 5/4
D. -5/4
,Correct Answer: A
Rationale: The slope formula is m = (y₂ - y₁)/(x₂ - x₁). Using the given points, we
substitute: m = (1 - 5)/(-3 - 2) = (-4)/(-5) = 4/5. The slope is positive because as x
increases, y also increases. We can verify this by checking that moving from (2, 5)
to (-3, 1) represents a rise of -4 units and a run of -5 units, giving us the same slope
of 4/5.
3. Solve the inequality: 2x - 5 > 3x + 2
A. x > -7
B. x < -7
C. x > 7
D. x < 7
Correct Answer: B
Rationale: To solve this inequality, we need to isolate x. First, subtract 3x from
both sides: 2x - 3x - 5 > 2, which gives us -x - 5 > 2. Then add 5 to both sides: -x >
7. Finally, multiply both sides by -1, remembering to reverse the inequality sign
when multiplying by a negative number: x < -7. We can test this by substituting x =
-8: 2(-8) - 5 = -21 and 3(-8) + 2 = -22, and -21 > -22 is true.
4. Factor completely: x² - 9x + 20
A. (x - 4)(x - 5)
B. (x + 4)(x + 5)
C. (x - 2)(x - 10)
D. (x + 2)(x + 10)
Correct Answer: A
Rationale: To factor this quadratic expression, we need to find two numbers that
multiply to 20 and add to -9. These numbers are -4 and -5. Therefore, x² - 9x + 20
,= (x - 4)(x - 5). We can verify this by expanding: (x - 4)(x - 5) = x² - 5x - 4x + 20 =
x² - 9x + 20, which matches our original expression.
5. Solve the system of equations:
x+y=7
2x - y = 5
A. (4, 3)
B. (3, 4)
C. (5, 2)
D. (2, 5)
Correct Answer: A
Rationale: We can solve this system using the elimination method. Adding the two
equations together eliminates y: (x + y) + (2x - y) = 7 + 5, giving us 3x = 12, so x =
4. Substituting x = 4 into the first equation: 4 + y = 7, therefore y = 3. The solution
is (4, 3). We can verify this by checking both equations: 4 + 3 = 7 ✓ and 2(4) - 3 =
8 - 3 = 5 ✓.
6. Simplify: (3x²y³)²
A. 9x⁴y⁶
B. 6x⁴y⁶
C. 9x⁴y⁵
D. 3x⁴y⁶
Correct Answer: A
Rationale: When raising a product to a power, we raise each factor to that power.
Using the exponent rule (ab)ⁿ = aⁿbⁿ and (aᵐ)ⁿ = aᵐⁿ: (3x²y³)² = 3²(x²)²(y³)² = 9x⁴y⁶.
The coefficient 3 becomes 9 (3²), x² becomes x⁴ (x²•²), and y³ becomes y⁶ (y³•²).
, 7. Solve for x: x² - 6x + 8 = 0
A. x = 2, 4
B. x = -2, -4
C. x = 1, 8
D. x = -1, -8
Correct Answer: A
Rationale: This quadratic equation can be solved by factoring. We need two
numbers that multiply to 8 and add to -6, which are -2 and -4. So x² - 6x + 8 = (x -
2)(x - 4) = 0. Using the zero product property, either x - 2 = 0 (giving x = 2) or x -
4 = 0 (giving x = 4). We can verify: (2)² - 6(2) + 8 = 4 - 12 + 8 = 0 ✓ and (4)² -
6(4) + 8 = 16 - 24 + 8 = 0 ✓.
8. Find the x-intercept of the line 2x + 3y = 12
A. (6, 0)
B. (4, 0)
C. (0, 4)
D. (0, 6)
Correct Answer: A
Rationale: The x-intercept occurs where y = 0. Substituting y = 0 into the equation:
2x + 3(0) = 12, which simplifies to 2x = 12. Dividing both sides by 2 gives x = 6.
Therefore, the x-intercept is (6, 0). We can verify this by substituting back: 2(6) +
3(0) = 12 + 0 = 12 ✓.
9. Simplify: √(50x²y)
A. 5x√(2y)
B. 5xy√2
– Complete 70 Questions, Correct
Answers & Detailed Rationales (2025 /
2026 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: To solve this linear equation, we need to isolate x on one side. First,
subtract 2x from both sides: 3x - 2x - 7 = 5, which simplifies to x - 7 = 5. Then add
7 to both sides: x = 12. We can verify this by substituting x = 12 back into the
original equation: 3(12) - 7 = 36 - 7 = 29 and 2(12) + 5 = 24 + 5 = 29. Since both
sides equal 29, our solution is correct.
2. Find the slope of the line passing through points (2, 5) and (-3, 1)
A. 4/5
B. -4/5
C. 5/4
D. -5/4
,Correct Answer: A
Rationale: The slope formula is m = (y₂ - y₁)/(x₂ - x₁). Using the given points, we
substitute: m = (1 - 5)/(-3 - 2) = (-4)/(-5) = 4/5. The slope is positive because as x
increases, y also increases. We can verify this by checking that moving from (2, 5)
to (-3, 1) represents a rise of -4 units and a run of -5 units, giving us the same slope
of 4/5.
3. Solve the inequality: 2x - 5 > 3x + 2
A. x > -7
B. x < -7
C. x > 7
D. x < 7
Correct Answer: B
Rationale: To solve this inequality, we need to isolate x. First, subtract 3x from
both sides: 2x - 3x - 5 > 2, which gives us -x - 5 > 2. Then add 5 to both sides: -x >
7. Finally, multiply both sides by -1, remembering to reverse the inequality sign
when multiplying by a negative number: x < -7. We can test this by substituting x =
-8: 2(-8) - 5 = -21 and 3(-8) + 2 = -22, and -21 > -22 is true.
4. Factor completely: x² - 9x + 20
A. (x - 4)(x - 5)
B. (x + 4)(x + 5)
C. (x - 2)(x - 10)
D. (x + 2)(x + 10)
Correct Answer: A
Rationale: To factor this quadratic expression, we need to find two numbers that
multiply to 20 and add to -9. These numbers are -4 and -5. Therefore, x² - 9x + 20
,= (x - 4)(x - 5). We can verify this by expanding: (x - 4)(x - 5) = x² - 5x - 4x + 20 =
x² - 9x + 20, which matches our original expression.
5. Solve the system of equations:
x+y=7
2x - y = 5
A. (4, 3)
B. (3, 4)
C. (5, 2)
D. (2, 5)
Correct Answer: A
Rationale: We can solve this system using the elimination method. Adding the two
equations together eliminates y: (x + y) + (2x - y) = 7 + 5, giving us 3x = 12, so x =
4. Substituting x = 4 into the first equation: 4 + y = 7, therefore y = 3. The solution
is (4, 3). We can verify this by checking both equations: 4 + 3 = 7 ✓ and 2(4) - 3 =
8 - 3 = 5 ✓.
6. Simplify: (3x²y³)²
A. 9x⁴y⁶
B. 6x⁴y⁶
C. 9x⁴y⁵
D. 3x⁴y⁶
Correct Answer: A
Rationale: When raising a product to a power, we raise each factor to that power.
Using the exponent rule (ab)ⁿ = aⁿbⁿ and (aᵐ)ⁿ = aᵐⁿ: (3x²y³)² = 3²(x²)²(y³)² = 9x⁴y⁶.
The coefficient 3 becomes 9 (3²), x² becomes x⁴ (x²•²), and y³ becomes y⁶ (y³•²).
, 7. Solve for x: x² - 6x + 8 = 0
A. x = 2, 4
B. x = -2, -4
C. x = 1, 8
D. x = -1, -8
Correct Answer: A
Rationale: This quadratic equation can be solved by factoring. We need two
numbers that multiply to 8 and add to -6, which are -2 and -4. So x² - 6x + 8 = (x -
2)(x - 4) = 0. Using the zero product property, either x - 2 = 0 (giving x = 2) or x -
4 = 0 (giving x = 4). We can verify: (2)² - 6(2) + 8 = 4 - 12 + 8 = 0 ✓ and (4)² -
6(4) + 8 = 16 - 24 + 8 = 0 ✓.
8. Find the x-intercept of the line 2x + 3y = 12
A. (6, 0)
B. (4, 0)
C. (0, 4)
D. (0, 6)
Correct Answer: A
Rationale: The x-intercept occurs where y = 0. Substituting y = 0 into the equation:
2x + 3(0) = 12, which simplifies to 2x = 12. Dividing both sides by 2 gives x = 6.
Therefore, the x-intercept is (6, 0). We can verify this by substituting back: 2(6) +
3(0) = 12 + 0 = 12 ✓.
9. Simplify: √(50x²y)
A. 5x√(2y)
B. 5xy√2
