Major Competitive Exams
Q. Solve the inequality 3x + 5 < 2x + 8.
-
A.
x < 3
-
B.
x > 3
-
C.
x < 2
-
D.
x > 2
Solution
3x + 5 < 2x + 8 => x < 3.
Correct Answer: A — x < 3
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Q. Solve the inequality 3x - 4 < 2x + 1.
-
A.
x < 5
-
B.
x > 5
-
C.
x ≤ 5
-
D.
x ≥ 5
Solution
3x - 4 < 2x + 1 => x < 5.
Correct Answer: A — x < 5
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Q. Solve the inequality 3x - 7 < 2x + 1.
-
A.
x < 8
-
B.
x > 8
-
C.
x < 6
-
D.
x > 6
Solution
3x - 7 < 2x + 1 => x < 8.
Correct Answer: C — x < 6
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Q. Solve the inequality 4 - 2x ≤ 10. What is the solution?
-
A.
x ≥ -3
-
B.
x ≤ -3
-
C.
x > -3
-
D.
x < -3
Solution
4 - 2x ≤ 10 => -2x ≤ 6 => x ≥ -3.
Correct Answer: A — x ≥ -3
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Q. Solve the inequality 4 - x > 2x + 1. What is the solution?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
4 - x > 2x + 1 => 3 > 3x => x < 1.
Correct Answer: A — x < 1
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Q. Solve the inequality 4 - x ≤ 2.
-
A.
x ≥ 2
-
B.
x ≤ 2
-
C.
x > 2
-
D.
x < 2
Solution
4 - x ≤ 2 => -x ≤ -2 => x ≥ 2.
Correct Answer: B — x ≤ 2
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Q. Solve the inequality 4 - x ≤ 2x + 1. What is the solution?
-
A.
x ≤ 1
-
B.
x ≥ 1
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
4 - x ≤ 2x + 1 => 3 ≤ 3x => x ≥ 1.
Correct Answer: A — x ≤ 1
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Q. Solve the inequality 4x + 5 > 3x + 10. What is the solution?
-
A.
x < 5
-
B.
x > 5
-
C.
x < 10
-
D.
x > 10
Solution
4x + 5 > 3x + 10 => x > 5.
Correct Answer: B — x > 5
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Q. Solve the inequality 4x - 1 > 3x + 2. What is the solution?
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
4x - 1 > 3x + 2 => x > 3.
Correct Answer: B — x > 3
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Q. Solve the inequality 4x - 1 < 3x + 2.
-
A.
x < 3
-
B.
x > 3
-
C.
x < 1
-
D.
x > 1
Solution
4x - 1 < 3x + 2 => x < 3.
Correct Answer: A — x < 3
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Q. Solve the inequality 4x - 1 ≥ 3x + 2. What is the solution?
-
A.
x ≥ 3
-
B.
x ≤ 3
-
C.
x ≥ 1
-
D.
x ≤ 1
Solution
4x - 1 ≥ 3x + 2 => x ≥ 3.
Correct Answer: C — x ≥ 1
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Q. Solve the inequality 4x - 7 > 9.
-
A.
x > 4
-
B.
x < 4
-
C.
x > 3
-
D.
x < 3
Solution
4x - 7 > 9 => 4x > 16 => x > 4.
Correct Answer: C — x > 3
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Q. Solve the inequality 4x - 7 < 9.
-
A.
x < 4
-
B.
x < 3
-
C.
x > 4
-
D.
x > 3
Solution
4x - 7 < 9 => 4x < 16 => x < 4.
Correct Answer: B — x < 3
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Q. Solve the inequality 4x - 7 ≥ 9.
-
A.
x ≥ 4
-
B.
x ≤ 4
-
C.
x > 4
-
D.
x < 4
Solution
4x - 7 ≥ 9 => 4x ≥ 16 => x ≥ 4.
Correct Answer: A — x ≥ 4
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Q. Solve the inequality 5 - 2x > 1. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
5 - 2x > 1 => -2x > -4 => x < 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 5 - 2x > 3.
-
A.
x < 1
-
B.
x > 1
-
C.
x < -1
-
D.
x > -1
Solution
5 - 2x > 3 => -2x > -2 => x < 1.
Correct Answer: B — x > 1
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Q. Solve the inequality 5 - 2x ≤ 3. What is the solution?
-
A.
x ≥ 1
-
B.
x ≤ 1
-
C.
x > 1
-
D.
x < 1
Solution
5 - 2x ≤ 3 => -2x ≤ -2 => x ≥ 1.
Correct Answer: B — x ≤ 1
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Q. Solve the inequality 5 - 2x ≥ 3.
-
A.
x ≤ 1
-
B.
x ≥ 1
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
5 - 2x ≥ 3 => -2x ≥ -2 => x ≤ 1.
Correct Answer: B — x ≥ 1
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Q. Solve the inequality 5 - x ≤ 2.
-
A.
x ≥ 3
-
B.
x ≤ 3
-
C.
x > 3
-
D.
x < 3
Solution
5 - x ≤ 2 => -x ≤ -3 => x ≥ 3.
Correct Answer: B — x ≤ 3
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Q. Solve the inequality 5 - x ≥ 1.
-
A.
x ≤ 4
-
B.
x < 4
-
C.
x ≥ 4
-
D.
x > 4
Solution
5 - x ≥ 1 => -x ≥ -4 => x ≤ 4.
Correct Answer: A — x ≤ 4
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Q. Solve the inequality 5x - 7 > 3x + 1.
-
A.
x > 4
-
B.
x < 4
-
C.
x > 2
-
D.
x < 2
Solution
5x - 7 > 3x + 1 => 2x > 8 => x > 4.
Correct Answer: C — x > 2
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Q. Solve the inequality 6 - 2x > 4.
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
6 - 2x > 4 => -2x > -2 => x < 1.
Correct Answer: B — x > 1
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Q. Solve the inequality 6 - 2x > 4. What is the solution?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
6 - 2x > 4 => -2x > -2 => x < 1.
Correct Answer: B — x > 1
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Q. Solve the inequality 6 - 2x ≤ 4.
-
A.
x ≥ 1
-
B.
x < 1
-
C.
x > 1
-
D.
x ≤ 1
Solution
6 - 2x ≤ 4 => -2x ≤ -2 => x ≥ 1.
Correct Answer: D — x ≤ 1
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Q. Solve the inequality 6 - 3x ≤ 0.
-
A.
x ≥ 2
-
B.
x < 2
-
C.
x > 2
-
D.
x ≤ 2
Solution
Subtract 6 from both sides: -3x ≤ -6. Then divide by -3 (reverse the inequality): x ≥ 2.
Correct Answer: A — x ≥ 2
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Q. Solve the inequality 6 - 3x ≥ 0. What is the solution?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer: B — x ≥ 2
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Q. Solve the inequality 6x + 2 < 14.
-
A.
x < 2
-
B.
x < 3
-
C.
x > 2
-
D.
x > 3
Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer: B — x < 3
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Q. Solve the inequality 7 - 3x > 1.
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
7 - 3x > 1 => -3x > -6 => x < 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7 - 3x > 1. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7 - 3x > 1 => -3x > -6 => x > 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7 - 3x < 1. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer: B — x > 2
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