Q. What is the solution to the equation 4x + 1 = 2x + 9?
-
A.
x = 4
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B.
x = 3
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C.
x = 2
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D.
x = 1
Solution
Subtract 2x from both sides: 2x + 1 = 9. Then subtract 1: 2x = 8. Finally, divide by 2: x = 4.
Correct Answer:
A
— x = 4
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Q. What is the solution to the equation 4x^2 - 16 = 0?
Solution
Step 1: Factor the equation: 4(x^2 - 4) = 0. Step 2: Set x^2 - 4 = 0: (x - 2)(x + 2) = 0. Step 3: Solutions are x = 2 or x = -2.
Correct Answer:
C
— 2
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Q. What is the solution to the equation 5(x - 2) = 3x + 4?
-
A.
x = 6
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B.
x = 5
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C.
x = 4
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D.
x = 3
Solution
Distribute: 5x - 10 = 3x + 4. Rearranging gives 2x = 14, so x = 7.
Correct Answer:
B
— x = 5
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Q. What is the value of x in the equation 3(x - 1) = 2(x + 2)?
Solution
Step 1: Distribute: 3x - 3 = 2x + 4. Step 2: Subtract 2x from both sides: x - 3 = 4. Step 3: Add 3 to both sides: x = 7.
Correct Answer:
B
— 0
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Q. What is the value of x in the equation 3x^2 + 12x + 12 = 0?
-
A.
x = -2
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B.
x = -4
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C.
x = 0
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D.
x = 2
Solution
Divide the equation by 3: x^2 + 4x + 4 = 0. Factor: (x + 2)(x + 2) = 0, giving x = -2.
Correct Answer:
B
— x = -4
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Q. What is the value of x in the equation x^2 - 5x + 6 = 0?
Solution
Step 1: Factor the quadratic: (x - 2)(x - 3) = 0. Step 2: Set each factor to zero: x - 2 = 0 or x - 3 = 0. Step 3: Solutions are x = 2 or x = 3.
Correct Answer:
C
— 3
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Q. What is the value of x in the polynomial equation x^3 - 4x^2 + 4x = 0?
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A.
x = 0, 2
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B.
x = 1, 3
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C.
x = 2, 4
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D.
x = -1, 5
Solution
Factor out x: x(x^2 - 4x + 4) = 0. This gives x = 0 or (x - 2)^2 = 0, so x = 2.
Correct Answer:
A
— x = 0, 2
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Q. Which of the following is the correct factorization of x^2 + 5x + 6?
-
A.
(x + 2)(x + 3)
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B.
(x - 2)(x - 3)
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C.
(x + 1)(x + 6)
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D.
(x - 1)(x - 6)
Solution
Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3. Step 2: Factor as (x + 2)(x + 3).
Correct Answer:
A
— (x + 2)(x + 3)
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