Q. What is the slope of the line represented by the equation 2y = 4x + 6?
Solution
Step 1: Rewrite in slope-intercept form: y = 2x + 3. Step 2: The slope (m) is 2.
Correct Answer:
A
— 2
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Q. What is the slope of the line represented by the equation 4x - 2y = 8?
Solution
Rearranging to slope-intercept form: y = 2x - 4. The slope is 2.
Correct Answer:
C
— -2
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Q. What is the slope of the line that passes through the points (2, 3) and (5, 11)?
Solution
Slope = (11-3)/(5-2) = 8/3.
Correct Answer:
B
— 3
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Q. What is the solution set for the equation 2x + 3 = 7?
-
A.
x = 2
-
B.
x = 3
-
C.
x = 4
-
D.
x = 5
Solution
Subtract 3 from both sides: 2x = 4.\nThen divide by 2: x = 2.
Correct Answer:
A
— x = 2
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Q. What is the solution set for the equation 3x + 2 = 11?
-
A.
x = 3
-
B.
x = 4
-
C.
x = 5
-
D.
x = 2
Solution
To solve for x, subtract 2 from both sides: 3x = 9. Then divide by 3: x = 3.
Correct Answer:
B
— x = 4
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Q. What is the solution set for the equation 3x + 4 = 10?
-
A.
x = 2
-
B.
x = 3
-
C.
x = 4
-
D.
x = 1
Solution
To solve 3x + 4 = 10, subtract 4 from both sides: 3x = 6. Then divide by 3: x = 2.
Correct Answer:
A
— x = 2
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Q. What is the solution set for the equation 4x + 1 = 2x + 5?
-
A.
x = 2
-
B.
x = 1
-
C.
x = 0
-
D.
x = -2
Solution
Subtract 2x from both sides: 2x + 1 = 5. Then subtract 1: 2x = 4. Finally, divide by 2: x = 2.
Correct Answer:
A
— x = 2
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Q. What is the solution set for the equation 4x + 1 = 2x + 9?
-
A.
x = 4
-
B.
x = 3
-
C.
x = 2
-
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 set for the equation 4x + 8 = 0?
-
A.
x = -2
-
B.
x = 2
-
C.
x = 0
-
D.
x = 4
Solution
Subtract 8 from both sides: 4x = -8. Then divide by 4: x = -2.
Correct Answer:
A
— x = -2
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Q. What is the solution set for the equation x^2 - 9 = 0?
-
A.
x = 3, -3
-
B.
x = 9
-
C.
x = 0
-
D.
x = 1, -1
Solution
Factoring gives (x - 3)(x + 3) = 0. Thus, the solutions are x = 3 and x = -3.
Correct Answer:
A
— x = 3, -3
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Q. What is the solution set for the inequality 2x + 1 ≥ 3?
-
A.
x ≥ 1
-
B.
x ≤ 1
-
C.
x > 1
-
D.
x < 1
Solution
Subtract 1 from both sides: 2x ≥ 2. Then divide by 2: x ≥ 1.
Correct Answer:
A
— x ≥ 1
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Q. What is the solution set for the inequality 2x + 1 ≥ 5?
-
A.
x ≥ 2
-
B.
x ≤ 2
-
C.
x > 2
-
D.
x < 2
Solution
Subtract 1 from both sides: 2x ≥ 4. Then divide by 2: x ≥ 2.
Correct Answer:
A
— x ≥ 2
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Q. What is the solution set for the inequality 2x + 3 ≥ 7?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
Subtract 3 from both sides: 2x ≥ 4. Then divide by 2: x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Q. What is the solution set for the inequality 2x + 5 > 3?
-
A.
x > -1
-
B.
x < -1
-
C.
x > 1
-
D.
x < 1
Solution
Step 1: Subtract 5 from both sides: 2x > -2. Step 2: Divide by 2: x > -1.
Correct Answer:
A
— x > -1
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Q. What is the solution set for the inequality 2x - 3 < 5?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 1
-
D.
x > 1
Solution
First, add 3 to both sides: 2x < 8. Then divide by 2: x < 4.
Correct Answer:
A
— x < 4
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Q. What is the solution set for the inequality 2x - 4 < 0?
-
A.
x < 2
-
B.
x > 2
-
C.
x = 2
-
D.
x ≤ 2
Solution
Solving the inequality: 2x < 4, thus x < 2.
Correct Answer:
A
— x < 2
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Q. What is the solution set for the inequality 2x - 4 < 6?
-
A.
x < 5
-
B.
x > 5
-
C.
x < 2
-
D.
x > 2
Solution
Add 4 to both sides: 2x < 10. Then divide by 2: x < 5.
Correct Answer:
A
— x < 5
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Q. What is the solution set for the inequality 2x - 5 < 3?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 2
-
D.
x > 2
Solution
Add 5 to both sides: 2x < 8. Then divide by 2: x < 4.
Correct Answer:
A
— x < 4
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Q. What is the solution set for the inequality 3x - 4 < 5?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 1
-
D.
x > 1
Solution
Add 4 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. What is the solution set for the inequality x + 2 > 3?
-
A.
x > 1
-
B.
x < 1
-
C.
x > 5
-
D.
x < 5
Solution
To solve x + 2 > 3, subtract 2 from both sides: x > 1.
Correct Answer:
A
— x > 1
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Q. What is the solution set for the inequality x + 2 > 5?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 7
-
D.
x > 7
Solution
Subtract 2 from both sides: x > 3.
Correct Answer:
B
— x > 3
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Q. What is the solution set for the inequality x + 5 > 2?
-
A.
x > -3
-
B.
x < -3
-
C.
x > 3
-
D.
x < 3
Solution
To solve x + 5 > 2, subtract 5 from both sides: x > -3.
Correct Answer:
A
— x > -3
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Q. What is the solution set for the inequality x^2 - 4 > 0?
-
A.
(-∞, -2) ∪ (2, ∞)
-
B.
(-2, 2)
-
C.
[-2, 2]
-
D.
[2, ∞)
Solution
Factor the inequality: (x - 2)(x + 2) > 0. The solution set is x < -2 or x > 2.
Correct Answer:
A
— (-∞, -2) ∪ (2, ∞)
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Q. What is the solution set for the inequality x^2 - 5x + 6 > 0?
-
A.
x < 2 or x > 3
-
B.
2 < x < 3
-
C.
x < 3
-
D.
x > 2
Solution
Factoring gives (x - 2)(x - 3) > 0. The roots are x = 2 and x = 3. The solution set is x < 2 or x > 3.
Correct Answer:
A
— x < 2 or x > 3
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Q. What is the solution set for the inequality: -4x + 1 < 3?
-
A.
x > -1/2
-
B.
x < -1/2
-
C.
x > 1/2
-
D.
x < 1/2
Solution
Step 1: Subtract 1 from both sides: -4x < 2. Step 2: Divide by -4 (reverse inequality): x > -1/2.
Correct Answer:
B
— x < -1/2
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Q. What is the solution set for the inequality: -4x + 1 ≤ 9?
-
A.
x ≥ -2
-
B.
x ≤ -2
-
C.
x > -2
-
D.
x < -2
Solution
Step 1: Subtract 1 from both sides: -4x ≤ 8. Step 2: Divide by -4 (reverse the inequality): x ≥ -2.
Correct Answer:
A
— x ≥ -2
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Q. What is the solution set for the inequality: 2x + 3 ≥ 11?
-
A.
x ≥ 4
-
B.
x ≤ 4
-
C.
x > 4
-
D.
x < 4
Solution
Step 1: Subtract 3 from both sides: 2x ≥ 8. Step 2: Divide both sides by 2: x ≥ 4.
Correct Answer:
A
— x ≥ 4
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Q. What is the solution set for the inequality: x^2 - 4 < 0?
-
A.
(-2, 2)
-
B.
(2, ∞)
-
C.
(-∞, -2)
-
D.
(-∞, 2)
Solution
Step 1: Factor: (x - 2)(x + 2) < 0. Step 2: Test intervals: solution is (-2, 2).
Correct Answer:
A
— (-2, 2)
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Q. What is the solution set for the inequality: x^2 - 5x + 6 < 0?
-
A.
(2, 3)
-
B.
(3, 2)
-
C.
(1, 6)
-
D.
(0, 5)
Solution
Step 1: Factor the quadratic: (x - 2)(x - 3) < 0. Step 2: Test intervals: solution is (2, 3).
Correct Answer:
A
— (2, 3)
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Q. What is the solution to the equation 2(x - 3) = 4?
-
A.
x = 1
-
B.
x = 2
-
C.
x = 4
-
D.
x = 7
Solution
2(x - 3) = 4. Divide by 2: x - 3 = 2. Add 3: x = 5.
Correct Answer:
D
— x = 7
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