Q. What is the solution to the inequality 4x + 1 > 3x + 5?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 3
-
D.
x > 3
Solution
Subtract 3x from both sides: x > 4.
Correct Answer: B — x > 4
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Q. What is the solution to the inequality 4x + 1 ≤ 3?
-
A.
x ≤ 0.5
-
B.
x < 0.5
-
C.
x ≥ 0.5
-
D.
x > 0.5
Solution
Subtract 1 from both sides: 4x ≤ 2. Then divide by 4: x ≤ 0.5.
Correct Answer: A — x ≤ 0.5
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Q. What is the solution to the inequality 4x + 5 < 3?
-
A.
x < -0.5
-
B.
x > -0.5
-
C.
x < -2
-
D.
x > -2
Solution
4x + 5 < 3 => 4x < -2 => x < -0.5.
Correct Answer: A — x < -0.5
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Q. What is the solution to the inequality 4x - 1 ≤ 3x + 2?
-
A.
x ≤ 3
-
B.
x ≥ 3
-
C.
x < 3
-
D.
x > 3
Solution
4x - 1 ≤ 3x + 2 => x ≤ 3.
Correct Answer: A — x ≤ 3
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Q. What is the solution to the inequality 4x - 5 < 3x + 2?
-
A.
x < 7
-
B.
x > 7
-
C.
x < -7
-
D.
x > -7
Solution
4x - 5 < 3x + 2 => x < 7.
Correct Answer: A — x < 7
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Q. What is the solution to the inequality 4x - 5 ≥ 3?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
4x - 5 ≥ 3 => 4x ≥ 8 => x ≥ 2.
Correct Answer: D — x ≥ 2
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Q. What is the solution to 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. What is the solution to the inequality 5 - 2x < 1?
-
A.
x > 2
-
B.
x < 2
-
C.
x > 3
-
D.
x < 3
Solution
Subtract 5 from both sides: -2x < -4. Then divide by -2 (reverse the inequality): x > 2.
Correct Answer: A — x > 2
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Q. What is the solution to the inequality 5 - 2x ≤ 1?
-
A.
x ≥ 2
-
B.
x ≤ 2
-
C.
x < 2
-
D.
x > 2
Solution
5 - 2x ≤ 1 => -2x ≤ -4 => x ≥ 2.
Correct Answer: A — x ≥ 2
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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
5 - 2x ≤ 3 => -2x ≤ -2 => x ≥ 1.
Correct Answer: B — x ≤ 1
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Q. What is the solution to the inequality 6 - 3x ≥ 0?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer: C — x ≤ 2
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Q. What is the solution to the inequality 6x + 2 < 14?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer: A — x < 2
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Q. What is the solution to the inequality 6x + 2 ≤ 14?
-
A.
x ≤ 2
-
B.
x < 2
-
C.
x ≥ 2
-
D.
x > 2
Solution
6x + 2 ≤ 14 => 6x ≤ 12 => x ≤ 2.
Correct Answer: A — x ≤ 2
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Q. What is the solution to the inequality 6x + 4 < 2x + 20?
-
A.
x < 4
-
B.
x > 4
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
6x + 4 < 2x + 20 => 4x < 16 => x < 4.
Correct Answer: A — x < 4
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Q. What is the solution to the inequality 6x + 4 ≤ 2x + 16?
-
A.
x ≤ 3
-
B.
x ≥ 3
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
6x + 4 ≤ 2x + 16 => 4x ≤ 12 => x ≤ 3.
Correct Answer: B — x ≥ 3
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Q. What is the solution to 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: A — x < 2
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Q. What is the solution to the inequality 7 - 3x < 1?
-
A.
x > 2
-
B.
x < 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer: A — x > 2
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Q. What is the solution to the inequality 7x + 2 > 5?
-
A.
x > 0.5
-
B.
x < 0.5
-
C.
x ≥ 0.5
-
D.
x ≤ 0.5
Solution
7x + 2 > 5 => 7x > 3 => x > 0.5.
Correct Answer: A — x > 0.5
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Q. What is the solution to the inequality 7x + 2 > 5x + 6?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7x + 2 > 5x + 6 => 2x > 4 => x > 2.
Correct Answer: B — x > 2
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Q. What is the solution to the inequality 7x + 2 < 5?
-
A.
x < -1
-
B.
x > -1
-
C.
x < 1
-
D.
x > 1
Solution
7x + 2 < 5 => 7x < 3 => x < -1.
Correct Answer: A — x < -1
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Q. What is the solution to the inequality 7x + 3 > 24?
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
7x + 3 > 24 => 7x > 21 => x > 3.
Correct Answer: B — x > 3
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Q. What is the solution to the inequality 7x + 5 < 2x + 20?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 4
-
D.
x > 4
Solution
7x + 5 < 2x + 20 => 5x < 15 => x < 3.
Correct Answer: A — x < 3
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Q. What is the solution to the inequality 7x - 4 < 3x + 8?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 2
-
D.
x > 2
Solution
7x - 4 < 3x + 8 => 4x < 12 => x < 3.
Correct Answer: B — x > 3
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Q. What is the solution to the inequality 8 - 2x > 0?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 2
-
D.
x > 2
Solution
8 - 2x > 0 => -2x > -8 => x < 4.
Correct Answer: B — x > 4
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Q. What is the solution to the inequality x/2 - 1 ≤ 3?
-
A.
x ≤ 8
-
B.
x ≥ 8
-
C.
x ≤ 6
-
D.
x ≥ 6
Solution
x/2 - 1 ≤ 3 => x/2 ≤ 4 => x ≤ 8.
Correct Answer: A — x ≤ 8
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Q. What is the solution to the inequality x/3 - 2 ≤ 1?
-
A.
x ≤ 9
-
B.
x ≥ 9
-
C.
x < 9
-
D.
x > 9
Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer: A — x ≤ 9
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Q. What is the specific heat capacity at constant volume (Cv) for a monatomic ideal gas?
-
A.
3/2 R
-
B.
5/2 R
-
C.
R
-
D.
2 R
Solution
The specific heat capacity at constant volume for a monatomic ideal gas is Cv = 3/2 R.
Correct Answer: A — 3/2 R
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Q. What is the specific heat capacity of a substance?
-
A.
The amount of heat required to change its temperature by 1 degree Celsius
-
B.
The amount of heat required to change its state
-
C.
The heat required to raise the temperature of a unit mass by 1 degree Celsius
-
D.
The heat required to cool a substance
Solution
The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of a unit mass by 1 degree Celsius.
Correct Answer: C — The heat required to raise the temperature of a unit mass by 1 degree Celsius
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Q. What is the specific heat capacity of water if 500 J of heat is required to raise the temperature of 100 g of water by 5°C?
-
A.
1 J/g°C
-
B.
2 J/g°C
-
C.
4 J/g°C
-
D.
5 J/g°C
Solution
Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (100 g * 5°C) = 1 J/g°C.
Correct Answer: A — 1 J/g°C
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Q. What is the specific heat capacity of water?
-
A.
1 J/g°C
-
B.
4.18 J/g°C
-
C.
2 J/g°C
-
D.
0.5 J/g°C
Solution
The specific heat capacity of water is approximately 4.18 J/g°C.
Correct Answer: B — 4.18 J/g°C
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