Q. If 2x + 5 = 3x - 1, what is the value of x?
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Solution
Rearranging gives: 5 + 1 = 3x - 2x, thus x = 6.
Correct Answer:
A
— -6
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Q. Solve for x: 4(x - 1) = 2(x + 3).
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Solution
Step 1: Distribute: 4x - 4 = 2x + 6. Step 2: Subtract 2x from both sides: 2x - 4 = 6. Step 3: Add 4 to both sides: 2x = 10. Step 4: Divide by 2: x = 5.
Correct Answer:
C
— 1
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Q. Solve for x: x^2 - 5x + 6 = 0.
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Solution
Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.
Correct Answer:
B
— 2
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Q. What is the product of (x + 1)(x + 4)?
A.
x^2 + 5x + 4
B.
x^2 + 3x + 4
C.
x^2 + 4x + 1
D.
x^2 + 5x + 1
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Solution
Step 1: Use the distributive property: x^2 + 4x + x + 4. Step 2: Combine like terms: x^2 + 5x + 4.
Correct Answer:
A
— x^2 + 5x + 4
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Q. What is the result of (2x + 3)(x - 1)?
A.
2x^2 + x - 3
B.
2x^2 + 5x - 3
C.
2x^2 - x + 3
D.
2x^2 - 5x - 3
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Solution
Step 1: Use the distributive property: 2x^2 - 2x + 3x - 3. Step 2: Combine like terms: 2x^2 + x - 3.
Correct Answer:
B
— 2x^2 + 5x - 3
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Q. What is the result of (x + 2)(x - 3)?
A.
x^2 - x - 6
B.
x^2 + x - 6
C.
x^2 - 6
D.
x^2 + 6
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Solution
Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.
Correct Answer:
A
— x^2 - x - 6
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Q. What is the sum of the roots of the quadratic equation x^2 + 4x + 4 = 0?
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Solution
The sum of the roots is given by -b/a = -4/1 = -4.
Correct Answer:
A
— -4
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Q. What is the value of x in the equation 4x^2 - 12x + 9 = 0?
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Solution
Factor the equation: (2x - 3)(2x - 3) = 0. Thus, x = 3.
Correct Answer:
C
— 3
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Q. What is the vertex of the parabola given by the equation y = x^2 - 4x + 3?
A.
(2, -1)
B.
(2, 1)
C.
(1, 2)
D.
(3, 0)
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Solution
Step 1: Use the vertex formula x = -b/(2a): x = 4/(2*1) = 2. Step 2: Substitute x back into the equation: y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1. Step 3: Vertex is (2, -1).
Correct Answer:
A
— (2, -1)
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Q. Which expression represents the difference of squares for a^2 - b^2?
A.
(a + b)(a - b)
B.
(a - b)(a + b)
C.
(a + b)^2
D.
(a - b)^2
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Solution
The difference of squares is factored as (a + b)(a - b).
Correct Answer:
A
— (a + b)(a - b)
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Q. Which of the following is a solution to the inequality 2x + 3 > 7?
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Solution
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2. The solution includes all values greater than 2.
Correct Answer:
B
— 2
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Q. Which of the following is a solution to the inequality 3x - 4 < 5?
A.
x < 3
B.
x > 3
C.
x < 2
D.
x > 2
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Solution
Add 4 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
A
— x < 3
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