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