Q. Solve 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. Solve the inequality 3x - 5 < 4.
-
A.
x < 3
-
B.
x < 2
-
C.
x > 3
-
D.
x > 2
Solution
Step 1: Add 5 to both sides: 3x < 9. Step 2: Divide by 3: x < 3.
Correct Answer:
B
— x < 2
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Q. Solve the inequality 3x - 5 < 7.
-
A.
x < 4
-
B.
x > 4
-
C.
x < 2
-
D.
x > 2
Solution
To solve 3x - 5 < 7, add 5 to both sides: 3x < 12. Then divide by 3: x < 4.
Correct Answer:
A
— x < 4
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Q. Solve the inequality 3x - 7 < 2.
-
A.
x < 3
-
B.
x < 2
-
C.
x > 3
-
D.
x > 2
Solution
To solve 3x - 7 < 2, add 7 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. Solve the inequality 5x - 2 < 3.
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Add 2 to both sides: 5x < 5. Step 2: Divide both sides by 5: x < 1.
Correct Answer:
A
— x < 1
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Q. Solve the inequality 5x - 7 < 3.
-
A.
x < 2
-
B.
x > 2
-
C.
x < 1
-
D.
x > 1
Solution
Step 1: Add 7 to both sides: 5x < 10. Step 2: Divide by 5: x < 2.
Correct Answer:
A
— x < 2
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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: -3x + 4 > 2.
-
A.
x < 2/3
-
B.
x > 2/3
-
C.
x ≤ 2/3
-
D.
x ≥ 2/3
Solution
Step 1: Subtract 4 from both sides: -3x > -2. Step 2: Divide by -3 (reverse the inequality): x < 2/3.
Correct Answer:
B
— x > 2/3
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Q. Solve the inequality: -3x + 7 ≤ 1.
-
A.
x ≥ 2
-
B.
x ≤ 2
-
C.
x > 2
-
D.
x < 2
Solution
Step 1: Subtract 7 from both sides: -3x ≤ -6. Step 2: Divide by -3 (reverse the inequality): x ≥ 2.
Correct Answer:
B
— x ≤ 2
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Q. Solve 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. Solve the inequality: 2(x - 1) ≥ 3x + 4.
-
A.
x ≤ -2
-
B.
x ≥ -2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
Step 1: Distribute: 2x - 2 ≥ 3x + 4. Step 2: Subtract 2x from both sides: -2 ≥ x + 4. Step 3: Subtract 4: -6 ≥ x. Step 4: Reverse: x ≤ -6.
Correct Answer:
A
— x ≤ -2
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Q. Solve the inequality: 2(x - 3) ≤ 4.
-
A.
x ≤ 5
-
B.
x ≥ 5
-
C.
x < 5
-
D.
x > 5
Solution
Step 1: Distribute: 2x - 6 ≤ 4. Step 2: Add 6 to both sides: 2x ≤ 10. Step 3: Divide by 2: x ≤ 5.
Correct Answer:
A
— x ≤ 5
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Q. Solve the inequality: 2x - 3 < 7
-
A.
x < 5
-
B.
x > 5
-
C.
x < 2
-
D.
x > 2
Solution
Add 3 to both sides: 2x < 10. Then divide by 2: x < 5.
Correct Answer:
A
— x < 5
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Q. Solve the inequality: 2x - 5 < 3
-
A.
x < 4
-
B.
x < 3
-
C.
x < 2
-
D.
x < 1
Solution
Add 5 to both sides: 2x < 8. Divide by 2: x < 4.
Correct Answer:
A
— x < 4
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Q. Solve the inequality: 3x + 4 > 10
-
A.
x > 2
-
B.
x < 2
-
C.
x > 3
-
D.
x < 3
Solution
Subtract 4 from both sides: 3x > 6. Then divide by 3: x > 2.
Correct Answer:
A
— x > 2
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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: 4x - 7 > 2x + 5.
-
A.
x > 6
-
B.
x < 6
-
C.
x > 5
-
D.
x < 5
Solution
Step 1: Subtract 2x from both sides: 2x - 7 > 5. Step 2: Add 7: 2x > 12. Step 3: Divide by 2: x > 6.
Correct Answer:
A
— x > 6
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Q. Solve the inequality: 6 - 3x < 0.
-
A.
x > 2
-
B.
x < 2
-
C.
x > -2
-
D.
x < -2
Solution
Step 1: Subtract 6 from both sides: -3x < -6. Step 2: Divide by -3 (reverse inequality): x > 2.
Correct Answer:
A
— x > 2
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Q. Solve the inequality: 7 - 2x < 1.
-
A.
x > 3
-
B.
x < 3
-
C.
x > 4
-
D.
x < 4
Solution
Step 1: Subtract 7 from both sides: -2x < -6. Step 2: Divide by -2 (reverse the inequality): x > 3.
Correct Answer:
B
— x < 3
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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 the inequality): x > 2.
Correct Answer:
A
— 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: 7x + 2 ≤ 3x + 10.
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Subtract 3x from both sides: 4x + 2 ≤ 10. Step 2: Subtract 2: 4x ≤ 8. Step 3: Divide by 4: x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Q. Solve the inequality: x^2 + 2x - 8 < 0.
-
A.
-4 < x < 2
-
B.
x < -4 or x > 2
-
C.
x > -4 and x < 2
-
D.
x < 2
Solution
Step 1: Factor: (x + 4)(x - 2) < 0. Step 2: Critical points are x = -4 and x = 2. Step 3: Test intervals: -4 < x < 2.
Correct Answer:
A
— -4 < x < 2
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Q. Solve the inequality: x^2 + 4x < 12.
-
A.
x < 2 or x > -6
-
B.
x > 2 and x < -6
-
C.
x < -2 or x > 6
-
D.
x > -6 and x < 2
Solution
Step 1: Rearrange: x^2 + 4x - 12 < 0. Step 2: Factor: (x + 6)(x - 2) < 0. Step 3: The solution is -6 < x < 2.
Correct Answer:
D
— x > -6 and x < 2
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Q. Solve the inequality: x^2 - 4 > 0.
-
A.
x < -2 or x > 2
-
B.
x > -2 and x < 2
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Factor: (x - 2)(x + 2) > 0. Step 2: Test intervals: solution is x < -2 or x > 2.
Correct Answer:
A
— x < -2 or x > 2
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Q. Solve the inequality: x^2 - 4x < 0.
-
A.
x < 0 or x > 4
-
B.
0 < x < 4
-
C.
x > 0
-
D.
x < 4
Solution
Step 1: Factor the inequality: x(x - 4) < 0. Step 2: The critical points are x = 0 and x = 4. Step 3: Test intervals: (0, 4) is the solution.
Correct Answer:
B
— 0 < x < 4
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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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Showing 1411 to 1440 of 2594 (87 Pages)
