Q. Solve for x in the equation 4(x - 1) = 2(x + 3).
-
A.
x = 5
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B.
x = 1
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C.
x = 2
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D.
x = 3
Solution
Distribute: 4x - 4 = 2x + 6. Subtract 2x from both sides: 2x - 4 = 6. Add 4: 2x = 10. Divide by 2: x = 5.
Correct Answer:
A
— x = 5
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Q. Solve for x: 5x + 2 > 12.
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
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D.
x > 3
Solution
Step 1: Subtract 2 from both sides: 5x > 10. Step 2: Divide both sides by 5: x > 2.
Correct Answer:
B
— x > 2
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Q. What is the factored form of the polynomial 2x^2 + 8x?
-
A.
2x(x + 4)
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B.
2(x + 4)(x + 2)
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C.
2x(x + 2)
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D.
2(x + 2)(x + 4)
Solution
Step 1: Factor out the common term: 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. What is the solution to the equation x^2 + 5x + 6 = 0?
-
A.
x = -2, -3
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B.
x = 2, 3
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C.
x = -1, -6
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D.
x = 1, 6
Solution
Step 1: Factor the equation: (x + 2)(x + 3) = 0. Step 2: Set each factor to zero: x + 2 = 0 or x + 3 = 0. Solutions are x = -2, -3.
Correct Answer:
A
— x = -2, -3
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Q. What is the solution to the inequality 2x + 3 ≥ 7?
-
A.
x ≤ 2
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B.
x ≥ 2
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C.
x < 2
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D.
x > 2
Solution
Step 1: Subtract 3 from both sides: 2x ≥ 4. Step 2: Divide by 2: x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Q. What is the value of x in the equation 4x - 7 = 5x + 2?
-
A.
x = -9
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B.
x = 11
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C.
x = 1
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D.
x = -1
Solution
Step 1: Subtract 4x from both sides: -7 = x + 2. Step 2: Subtract 2 from both sides: -9 = x. Therefore, x = -9.
Correct Answer:
C
— x = 1
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Q. What is the value of x in the equation 5(x - 1) = 3x + 7?
-
A.
x = 4
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B.
x = 5
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C.
x = 6
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D.
x = 3
Solution
Step 1: Distribute: 5x - 5 = 3x + 7. Step 2: Subtract 3x from both sides: 2x - 5 = 7. Step 3: Add 5: 2x = 12. Step 4: Divide by 2: x = 6.
Correct Answer:
A
— x = 4
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Q. What is the value of x in the equation x^2 - 16 = 0?
-
A.
x = 4
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B.
x = -4
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C.
x = 0
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D.
x = ±4
Solution
Factor the equation: (x - 4)(x + 4) = 0. Thus, x = 4 or x = -4.
Correct Answer:
D
— x = ±4
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Q. What is the vertex of the quadratic equation y = x^2 - 4x + 3?
-
A.
(2, -1)
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B.
(2, 1)
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C.
(1, 2)
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D.
(3, 0)
Solution
Step 1: Use the vertex formula x = -b/2a: x = 4/2 = 2. Step 2: Substitute x back into the equation: y = 2^2 - 4(2) + 3 = -1. Vertex is (2, -1).
Correct Answer:
A
— (2, -1)
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Q. Which expression represents the factored form of x^2 - 9?
-
A.
(x - 3)(x + 3)
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B.
(x - 1)(x + 1)
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C.
(x - 2)(x + 2)
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D.
(x - 4)(x + 4)
Solution
Step 1: Recognize it as a difference of squares: x^2 - 3^2. Step 2: Factor: (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. Which of the following represents the equation of a line with a slope of 2 and y-intercept of -3?
-
A.
y = 2x + 3
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B.
y = 2x - 3
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C.
y = -2x + 3
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D.
y = -2x - 3
Solution
The slope-intercept form is y = mx + b. Here, m = 2 and b = -3, so y = 2x - 3.
Correct Answer:
B
— y = 2x - 3
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