Q. If -x + 6 > 2, what is the solution for x?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 6
-
D.
x > 6
Solution
Step 1: Subtract 6 from both sides: -x > -4. Step 2: Multiply by -1 (reverse inequality): x < 4.
Correct Answer:
B
— x > 4
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Q. If 2x + 3 > 11, what is the solution for x?
-
A.
x > 4
-
B.
x < 4
-
C.
x > 3
-
D.
x < 3
Solution
Step 1: Subtract 3 from both sides: 2x > 8. Step 2: Divide by 2: x > 4.
Correct Answer:
A
— x > 4
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Q. If 2x + 5 > 3x - 1, what is the solution for x?
-
A.
x < 6
-
B.
x > 6
-
C.
x < -6
-
D.
x > -6
Solution
Step 1: Subtract 2x from both sides: 5 > x - 1. Step 2: Add 1: 6 > x, or x < 6.
Correct Answer:
D
— x > -6
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Q. If 3(x - 1) < 2x + 4, what is the solution for x?
-
A.
x < 7
-
B.
x > 7
-
C.
x < 5
-
D.
x > 5
Solution
Step 1: Distribute: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.
Correct Answer:
C
— x < 5
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Q. If 3(x - 1) < 2x + 4, what is the value of x?
-
A.
x < 7
-
B.
x > 7
-
C.
x < 1
-
D.
x > 1
Solution
Step 1: Distribute: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.
Correct Answer:
A
— x < 7
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Q. If 3x + 4 < 2x + 10, what is the value of x?
-
A.
x < 6
-
B.
x > 6
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Subtract 2x from both sides: x + 4 < 10. Step 2: Subtract 4: x < 6.
Correct Answer:
A
— x < 6
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Q. If 4x - 1 < 3x + 2, what is the value of x?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 1
-
D.
x > 1
Solution
Step 1: Subtract 3x from both sides: x - 1 < 2. Step 2: Add 1: x < 3.
Correct Answer:
A
— x < 3
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Q. If 5x - 2 ≤ 3, what is the maximum value of x?
-
A.
x ≤ 1
-
B.
x ≤ 2
-
C.
x ≤ 3
-
D.
x ≤ 4
Solution
Step 1: Add 2 to both sides: 5x ≤ 5. Step 2: Divide by 5: x ≤ 1.
Correct Answer:
A
— x ≤ 1
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Q. Solve the inequality: -2(x + 3) > 4.
-
A.
x < -1
-
B.
x > -1
-
C.
x < -7
-
D.
x > -7
Solution
Step 1: Distribute -2: -2x - 6 > 4. Step 2: Add 6: -2x > 10. Step 3: Divide by -2 (reverse inequality): x < -5.
Correct Answer:
C
— x < -7
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Q. Solve the inequality: -2(x + 3) > 6.
-
A.
x < -6
-
B.
x > -6
-
C.
x < 0
-
D.
x > 0
Solution
Step 1: Distribute: -2x - 6 > 6. Step 2: Add 6: -2x > 12. Step 3: Divide by -2 (reverse inequality): x < -6.
Correct Answer:
A
— x < -6
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Q. Solve the inequality: 4x + 1 ≥ 2x + 9.
-
A.
x ≥ 4
-
B.
x ≤ 4
-
C.
x ≥ 2
-
D.
x ≤ 2
Solution
Step 1: Subtract 2x from both sides: 2x + 1 ≥ 9. Step 2: Subtract 1: 2x ≥ 8. Step 3: Divide by 2: x ≥ 4.
Correct Answer:
A
— x ≥ 4
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Q. Solve the inequality: 7 - 2x ≥ 3.
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
Step 1: Subtract 7 from both sides: -2x ≥ -4. Step 2: Divide by -2 (reverse inequality): x ≤ 2.
Correct Answer:
B
— x ≥ 2
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Q. Solve the inequality: 7 - 3x ≥ 1.
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
Step 1: Subtract 7 from both sides: -3x ≥ -6. Step 2: Divide by -3 (reverse inequality): x ≤ 2.
Correct Answer:
B
— x ≥ 2
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Q. Solve the inequality: 7x + 1 ≤ 3x + 9.
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
Step 1: Subtract 3x from both sides: 4x + 1 ≤ 9. Step 2: Subtract 1: 4x ≤ 8. Step 3: Divide by 4: x ≤ 2.
Correct Answer:
A
— x ≤ 2
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Q. Solve the inequality: x^2 - 5x + 6 > 0.
-
A.
(2, 3)
-
B.
(3, ∞)
-
C.
(-∞, 2) ∪ (3, ∞)
-
D.
(2, ∞)
Solution
Step 1: Factor: (x - 2)(x - 3) > 0. Step 2: Test intervals: solution is (-∞, 2) ∪ (3, ∞).
Correct Answer:
C
— (-∞, 2) ∪ (3, ∞)
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Q. Solve the inequality: x^2 - 9 > 0.
-
A.
x < -3 or x > 3
-
B.
x > -3 and x < 3
-
C.
x < 3
-
D.
x > 3
Solution
Step 1: Factor: (x - 3)(x + 3) > 0. Step 2: Test intervals: solution is x < -3 or x > 3.
Correct Answer:
A
— x < -3 or x > 3
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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 to the inequality: 2(x - 1) < 3(x + 2)?
-
A.
x < 7
-
B.
x > 7
-
C.
x < 5
-
D.
x > 5
Solution
Step 1: Distribute: 2x - 2 < 3x + 6. Step 2: Subtract 2x: -2 < x + 6. Step 3: Subtract 6: -8 < x, or x > -8.
Correct Answer:
C
— x < 5
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Q. What is the solution to the inequality: x^2 - 9 > 0?
-
A.
x < -3 or x > 3
-
B.
-3 < x < 3
-
C.
x > -3 and x < 3
-
D.
x < 3
Solution
Step 1: Factor: (x - 3)(x + 3) > 0. Step 2: Test intervals: solution is x < -3 or x > 3.
Correct Answer:
A
— x < -3 or x > 3
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Q. Which of the following is a solution to 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 inequality): x ≥ -2.
Correct Answer:
A
— x ≤ -2
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Q. Which of the following represents the solution to the inequality: x^2 - 5x + 6 > 0?
-
A.
(2, 3)
-
B.
(3, ∞) ∪ (-∞, 2)
-
C.
(2, ∞)
-
D.
(3, 2)
Solution
Step 1: Factor: (x - 2)(x - 3) > 0. Step 2: Test intervals: solution is (3, ∞) ∪ (-∞, 2).
Correct Answer:
B
— (3, ∞) ∪ (-∞, 2)
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Q. Which of the following values satisfies the inequality: 3x + 4 < 10?
-
A.
x = 1
-
B.
x = 2
-
C.
x = 3
-
D.
x = 4
Solution
Step 1: Subtract 4 from both sides: 3x < 6. Step 2: Divide by 3: x < 2.
Correct Answer:
A
— x = 1
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Q. Which of the following values satisfies the inequality: 4 - x > 1?
-
A.
x < 3
-
B.
x > 3
-
C.
x = 3
-
D.
x ≤ 3
Solution
Step 1: Subtract 4 from both sides: -x > -3. Step 2: Multiply by -1 (reverse inequality): x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following values satisfies the inequality: 4x - 1 < 3x + 2?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 1
-
D.
x > 1
Solution
Step 1: Subtract 3x from both sides: x - 1 < 2. Step 2: Add 1: x < 3.
Correct Answer:
D
— x > 1
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