Q. Determine the solution for the inequality: 3(x - 1) < 2(x + 2).
A.
x < 5
B.
x > 5
C.
x < 1
D.
x > 1
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Solution
Step 1: Expand: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.
Correct Answer:
A
— x < 5
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Q. Determine the solution set for the inequality: 2x^2 - 8 < 0.
A.
(-2, 2)
B.
(2, -2)
C.
(-∞, -2) ∪ (2, ∞)
D.
(-2, ∞)
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Solution
Step 1: Factor the inequality: 2(x^2 - 4) < 0. Step 2: Roots are x = -2 and x = 2. Step 3: The solution is between the roots: (-2, 2).
Correct Answer:
A
— (-2, 2)
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Q. Determine the solution set for the inequality: x^2 + 4x + 3 < 0.
A.
(-3, -1)
B.
(-1, 3)
C.
(-∞, -3)
D.
(-∞, -1)
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Solution
Step 1: Factor the quadratic: (x + 3)(x + 1) < 0. Step 2: The critical points are x = -3 and x = -1. Step 3: Test intervals: The solution set is (-3, -1).
Correct Answer:
A
— (-3, -1)
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Q. Determine the solution set for the inequality: x^2 - 6x + 8 ≤ 0.
A.
[2, 4]
B.
(2, 4)
C.
[4, 2]
D.
(-∞, 2) ∪ (4, ∞)
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Solution
Step 1: Factor: (x - 2)(x - 4) ≤ 0. Step 2: The solution is between the roots: [2, 4].
Correct Answer:
A
— [2, 4]
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Q. Find the solution set for the inequality: 4x - 7 ≤ 9.
A.
x ≤ 4
B.
x ≥ 4
C.
x < 4
D.
x > 4
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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. Find the solution set for the inequality: x^2 + 2x - 8 > 0.
A.
(-∞, -4) ∪ (2, ∞)
B.
(-4, 2)
C.
(-2, 4)
D.
(-∞, 2) ∪ (4, ∞)
Show solution
Solution
Step 1: Factor the quadratic: (x - 2)(x + 4) > 0. Step 2: The solution is outside the roots: (-∞, -4) ∪ (2, ∞).
Correct Answer:
A
— (-∞, -4) ∪ (2, ∞)
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Q. Find the solution set for the inequality: x^2 + 3x - 4 > 0.
A.
(-∞, -4) ∪ (1, ∞)
B.
(-4, 1)
C.
(-∞, 1) ∪ (4, ∞)
D.
(-4, ∞)
Show solution
Solution
Step 1: Factor the quadratic: (x - 1)(x + 4) > 0. Step 2: The solution is outside the roots: (-∞, -4) ∪ (1, ∞).
Correct Answer:
A
— (-∞, -4) ∪ (1, ∞)
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Q. Find the solution set for the inequality: x^2 - 6x + 8 > 0.
A.
x < 2 or x > 4
B.
2 < x < 4
C.
x > 2
D.
x < 4
Show solution
Solution
Step 1: Factor: (x - 2)(x - 4) > 0. Step 2: Critical points are x = 2 and x = 4. Step 3: Test intervals: valid for x < 2 or x > 4.
Correct Answer:
A
— x < 2 or x > 4
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Q. Find the solution to the inequality: x^2 - 9 > 0.
A.
(-∞, -3) ∪ (3, ∞)
B.
(-3, 3)
C.
(-3, ∞)
D.
(-∞, 3)
Show solution
Solution
Step 1: Factor the inequality: (x - 3)(x + 3) > 0. Step 2: The critical points are x = -3 and x = 3. Step 3: Test intervals: The solution set is (-∞, -3) ∪ (3, ∞).
Correct Answer:
A
— (-∞, -3) ∪ (3, ∞)
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Q. If 3x + 2 < 5, what is the value of x?
A.
x < 1
B.
x > 1
C.
x < 2
D.
x > 2
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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. If 4x - 7 < 9, what is the maximum value of x?
Show solution
Solution
Step 1: Add 7 to both sides: 4x < 16. Step 2: Divide by 4: x < 4.
Correct Answer:
B
— 3
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Q. Solve the inequality: -3x + 7 ≤ 1.
A.
x ≥ 2
B.
x ≤ 2
C.
x > 2
D.
x < 2
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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: 6 - 3x < 0.
A.
x > 2
B.
x < 2
C.
x > -2
D.
x < -2
Show solution
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: 7x + 2 ≤ 3x + 10.
A.
x ≤ 2
B.
x ≥ 2
C.
x < 2
D.
x > 2
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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 quadratic inequality: x^2 - 5x + 6 < 0.
A.
1 < x < 6
B.
2 < x < 3
C.
x < 2 or x > 3
D.
2 < x < 6
Show solution
Solution
Step 1: Factor: (x - 2)(x - 3) < 0. Step 2: Test intervals: solution is 2 < x < 3.
Correct Answer:
B
— 2 < 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
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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
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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:
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
Show solution
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
Show solution
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)
Show solution
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: 3x + 2 > 5?
A.
x > 1
B.
x < 1
C.
x > 2
D.
x < 2
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: 4x - 1 < 3x + 2?
A.
x < 3
B.
x > 3
C.
x < 1
D.
x > 1
Show solution
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: 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:
B
— x > 1
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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
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. What is the solution to the inequality: x^2 + 4x < 5?
A.
x < 1 or x > -5
B.
x < -1 or x > 5
C.
x < -5 or x > 1
D.
x > -5 and x < 1
Show solution
Solution
Step 1: Rearrange: x^2 + 4x - 5 < 0. Step 2: Factor: (x + 5)(x - 1) < 0. Step 3: Solution is -5 < x < 1.
Correct Answer:
D
— x > -5 and x < 1
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Q. Which of the following is a solution to the inequality: -2x + 4 > 0?
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
Step 1: Subtract 4 from both sides: -2x > -4. Step 2: Divide by -2 (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: x^2 + 2x - 8 < 0?
A.
x < -4
B.
-4 < x < 2
C.
x > 2
D.
x = -4
Show solution
Solution
Step 1: Factor: (x + 4)(x - 2) < 0. Step 2: Critical points are x = -4 and x = 2. Step 3: Test intervals: valid for -4 < x < 2.
Correct Answer:
B
— -4 < x < 2
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Q. Which of the following is a solution to the inequality: x^2 - 4x < 0?
A.
x < 0
B.
0 < x < 4
C.
x > 4
D.
x = 2
Show solution
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 valid.
Correct Answer:
B
— 0 < x < 4
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Q. Which of the following is the solution to the inequality: -4x + 1 < 3?
A.
x > -1/2
B.
x < -1/2
C.
x > 1/2
D.
x < 1/2
Show solution
Solution
Step 1: Subtract 1 from both sides: -4x < 2. Step 2: Divide by -4 (reverse inequality): x > -1/2.
Correct Answer:
B
— x < -1/2
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Q. Which of the following represents the solution to the inequality: 4x - 1 < 3x + 2?
A.
x < 3
B.
x > 3
C.
x < 1
D.
x > 1
Show solution
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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