Q. What is the solution to the inequality 3x - 5 < 4?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 2
-
D.
x > 2
Solution
Add 5 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 to the inequality 3x - 7 < 2?
-
A.
x < 3
-
B.
x < 1
-
C.
x > 1
-
D.
x > 3
Solution
To solve 3x - 7 < 2, add 7 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
B
— x < 1
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Q. What is the solution to the inequality 4x - 8 < 0?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
4x - 8 < 0. Add 8 to both sides: 4x < 8. Divide by 4: x < 2.
Correct Answer:
A
— x < 2
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Q. What is the solution to the inequality 5x + 2 ≥ 12?
-
A.
x ≥ 2
-
B.
x ≤ 2
-
C.
x ≥ 3
-
D.
x ≤ 3
Solution
Subtract 2 from both sides: 5x ≥ 10. Then divide by 5: x ≥ 2.
Correct Answer:
C
— x ≥ 3
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Q. What is the solution to the inequality 5x + 3 > 2x + 12?
-
A.
x < 3
-
B.
x > 3
-
C.
x < -3
-
D.
x > -3
Solution
Subtract 2x from both sides: 3x + 3 > 12. Then subtract 3: 3x > 9. Finally, divide by 3: x > 3.
Correct Answer:
B
— x > 3
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Q. What is the solution to the inequality 5x - 2 < 3?
-
A.
x < 1
-
B.
x < 2
-
C.
x < 3
-
D.
x < 4
Solution
Add 2 to both sides: 5x < 5. Divide by 5: x < 1.
Correct Answer:
A
— x < 1
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Q. What is the solution to the inequality 5x - 3 < 12?
-
A.
x < 3
-
B.
x < 2
-
C.
x > 3
-
D.
x > 2
Solution
5x - 3 < 12. Add 3 to both sides: 5x < 15. Divide by 5: x < 3.
Correct Answer:
A
— x < 3
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Q. What is the solution to the inequality x + 5 > 2?
-
A.
x > -3
-
B.
x < -3
-
C.
x > 3
-
D.
x < 3
Solution
Subtract 5 from both sides: x > -3.
Correct Answer:
A
— x > -3
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Q. What is the solution to the inequality x^2 - 4 > 0?
-
A.
x < -2 or x > 2
-
B.
x > -2 and x < 2
-
C.
x < 2
-
D.
x > 4
Solution
Factoring gives (x - 2)(x + 2) > 0. The critical points are x = -2 and x = 2. The solution set is x < -2 or x > 2.
Correct Answer:
A
— x < -2 or x > 2
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Q. What is the solution to the inequality x^2 - 4 < 0?
-
A.
-2 < x < 2
-
B.
x < -2 or x > 2
-
C.
x > -2 and x < 2
-
D.
x = 0
Solution
Step 1: Factor the inequality: (x - 2)(x + 2) < 0. Step 2: The solution is between the roots: -2 < x < 2.
Correct Answer:
A
— -2 < x < 2
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Q. What is the solution to 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 to the inequality: -3x + 4 > 1?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 3
-
D.
x > 3
Solution
Step 1: Subtract 4 from both sides: -3x > -3. Step 2: Divide by -3 (reverse the inequality): x < 1.
Correct Answer:
D
— x > 3
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Q. What is the solution to the inequality: -3x + 6 ≤ 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 the inequality): x ≥ 2.
Correct Answer:
A
— x ≥ 2
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Q. What is the solution to the inequality: 2(x - 1) > 3(x + 2)?
-
A.
x < -1
-
B.
x > -1
-
C.
x < 1
-
D.
x > 1
Solution
Step 1: Distribute: 2x - 2 > 3x + 6. Step 2: Rearrange: -x > 8. Step 3: Divide by -1 (reverse inequality): x < -8.
Correct Answer:
A
— x < -1
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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: 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. Solution: x ≤ -6.
Correct Answer:
A
— x ≤ -2
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Q. What is the solution to the inequality: 2(x - 3) > 4?
-
A.
x > 5
-
B.
x < 5
-
C.
x > 1
-
D.
x < 1
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. What is the solution to 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: 2x ≥ 10. Step 3: Divide by 2: x ≥ 5.
Correct Answer:
A
— x ≥ 5
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Q. What is the solution to the inequality: 2x^2 - 8 < 0?
-
A.
(-2, 2)
-
B.
(2, -2)
-
C.
(0, 4)
-
D.
(4, 0)
Solution
Step 1: Factor: 2(x^2 - 4) < 0. Step 2: Further factor: 2(x - 2)(x + 2) < 0. Step 3: The solution is (-2, 2).
Correct Answer:
A
— (-2, 2)
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Q. What is the solution to the inequality: 3(x + 2) ≤ 2(x + 5)?
-
A.
x ≤ 1
-
B.
x ≥ 1
-
C.
x ≤ -1
-
D.
x ≥ -1
Solution
Step 1: Distribute: 3x + 6 ≤ 2x + 10. Step 2: Subtract 2x: x + 6 ≤ 10. Step 3: Subtract 6: x ≤ 4.
Correct Answer:
A
— x ≤ 1
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Q. What is the solution to the inequality: 3(x - 2) > 2(x + 1)?
-
A.
x > 1
-
B.
x < 1
-
C.
x > 2
-
D.
x < 2
Solution
Step 1: Distribute: 3x - 6 > 2x + 2. Step 2: Subtract 2x: x - 6 > 2. Step 3: Add 6: x > 8.
Correct Answer:
A
— x > 1
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Q. What is the solution to the inequality: 3x + 2 > 5?
-
A.
x > 1
-
B.
x < 1
-
C.
x > 2
-
D.
x < 2
Solution
Step 1: Subtract 2 from both sides: 3x > 3. Step 2: Divide by 3: x > 1.
Correct Answer:
A
— x > 1
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Q. What is the solution to the inequality: 3x + 2 ≤ 5?
-
A.
x ≤ 1
-
B.
x ≥ 1
-
C.
x < 1
-
D.
x > 1
Solution
Step 1: Subtract 2 from both sides: 3x ≤ 3. Step 2: Divide by 3: x ≤ 1.
Correct Answer:
A
— x ≤ 1
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Q. What is the solution to the inequality: 3x + 4 ≤ 2x + 10?
-
A.
x ≤ 6
-
B.
x ≤ 4
-
C.
x ≥ 6
-
D.
x ≥ 4
Solution
Step 1: Subtract 2x from both sides: x + 4 ≤ 10. Step 2: Subtract 4 from both sides: x ≤ 6.
Correct Answer:
A
— x ≤ 6
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Q. What is the solution to the inequality: 4x + 1 ≥ 2x + 9?
-
A.
x ≤ 4
-
B.
x ≥ 4
-
C.
x < 4
-
D.
x > 4
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:
B
— x ≥ 4
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Q. What is the solution to 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 to both sides: x < 3.
Correct Answer:
A
— x < 3
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Q. What is the solution to the inequality: 4x - 7 ≤ 9?
-
A.
x ≤ 4
-
B.
x ≥ 4
-
C.
x < 4
-
D.
x > 4
Solution
Step 1: Add 7 to both sides: 4x ≤ 16. Step 2: Divide by 4: x ≤ 4.
Correct Answer:
A
— x ≤ 4
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Q. What is the solution to the inequality: 5 - 2x > 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 (reverse inequality): x < 1.
Correct Answer:
B
— x > 1
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Q. What is the solution to the inequality: 6 - x < 2?
-
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 the inequality): x > 4.
Correct Answer:
A
— x > 4
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Q. What is the solution to 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:
A
— x < 3
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