Q. Solve the inequality 5 - 2x ≥ 3.
-
A.
x ≤ 1
-
B.
x ≥ 1
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
5 - 2x ≥ 3 => -2x ≥ -2 => x ≤ 1.
Correct Answer:
B
— x ≥ 1
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Q. Solve the inequality 5 - x ≤ 2.
-
A.
x ≥ 3
-
B.
x ≤ 3
-
C.
x > 3
-
D.
x < 3
Solution
5 - x ≤ 2 => -x ≤ -3 => x ≥ 3.
Correct Answer:
B
— x ≤ 3
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Q. Solve the inequality 5 - x ≥ 1.
-
A.
x ≤ 4
-
B.
x < 4
-
C.
x ≥ 4
-
D.
x > 4
Solution
5 - x ≥ 1 => -x ≥ -4 => x ≤ 4.
Correct Answer:
A
— x ≤ 4
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Q. Solve the inequality 5x - 7 > 3x + 1.
-
A.
x > 4
-
B.
x < 4
-
C.
x > 2
-
D.
x < 2
Solution
5x - 7 > 3x + 1 => 2x > 8 => x > 4.
Correct Answer:
C
— x > 2
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Q. Solve the inequality 6 - 2x > 4.
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
6 - 2x > 4 => -2x > -2 => x < 1.
Correct Answer:
B
— x > 1
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Q. Solve the inequality 6 - 2x > 4. What is the solution?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
6 - 2x > 4 => -2x > -2 => x < 1.
Correct Answer:
B
— x > 1
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Q. Solve the inequality 6 - 2x ≤ 4.
-
A.
x ≥ 1
-
B.
x < 1
-
C.
x > 1
-
D.
x ≤ 1
Solution
6 - 2x ≤ 4 => -2x ≤ -2 => x ≥ 1.
Correct Answer:
D
— x ≤ 1
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Q. Solve the inequality 6 - 3x ≤ 0.
-
A.
x ≥ 2
-
B.
x < 2
-
C.
x > 2
-
D.
x ≤ 2
Solution
Subtract 6 from both sides: -3x ≤ -6. Then divide by -3 (reverse the inequality): x ≥ 2.
Correct Answer:
A
— x ≥ 2
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Q. Solve the inequality 6 - 3x ≥ 0. What is the solution?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer:
B
— x ≥ 2
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Q. Solve the inequality 6x + 2 < 14.
-
A.
x < 2
-
B.
x < 3
-
C.
x > 2
-
D.
x > 3
Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer:
B
— x < 3
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Q. Solve 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:
B
— x > 2
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Q. Solve the inequality 7 - 3x > 1. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7 - 3x > 1 => -3x > -6 => x > 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality 7 - 3x < 1. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality 7 - x < 2.
-
A.
x > 5
-
B.
x < 5
-
C.
x > 7
-
D.
x < 7
Solution
7 - x < 2 => -x < -5 => x > 5.
Correct Answer:
A
— x > 5
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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
7x + 2 < 3x + 10 => 4x < 8 => x < 2.
Correct Answer:
B
— x > 2
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Q. Solve the inequality 7x - 4 < 2x + 11. What is the solution?
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
7x - 4 < 2x + 11 => 5x < 15 => x < 3.
Correct Answer:
B
— x > 3
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Q. Solve the inequality 7x - 5 < 2x + 10. What is the solution?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
7x - 5 < 2x + 10 => 5x < 15 => x < 3.
Correct Answer:
B
— x > 1
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Q. Solve the inequality 8 - x > 3.
-
A.
x < 5
-
B.
x > 5
-
C.
x < 3
-
D.
x > 3
Solution
8 - x > 3 => -x > -5 => x < 5.
Correct Answer:
A
— x < 5
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Q. Solve the inequality x/3 + 2 > 1. What is the solution?
-
A.
x > -3
-
B.
x < -3
-
C.
x > 3
-
D.
x < 3
Solution
x/3 + 2 > 1 => x/3 > -1 => x > -3.
Correct Answer:
C
— x > 3
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Q. Solve the inequality x/3 - 2 > 1. What is the solution set?
-
A.
x < 9
-
B.
x > 9
-
C.
x < 3
-
D.
x > 3
Solution
x/3 - 2 > 1 => x/3 > 3 => x > 9.
Correct Answer:
B
— x > 9
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Q. Solve the inequality x/3 - 2 ≤ 1. What is the solution?
-
A.
x ≤ 9
-
B.
x ≥ 9
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer:
A
— x ≤ 9
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Q. Solve the inequality x/4 - 1 < 0.
-
A.
x < 4
-
B.
x > 4
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
x/4 - 1 < 0 => x/4 < 1 => x < 4.
Correct Answer:
A
— x < 4
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Q. Solve the inequality: 4x + 1 ≥ 3.
-
A.
x ≥ 0.5
-
B.
x ≤ 0.5
-
C.
x ≥ 1
-
D.
x ≤ 1
Solution
4x + 1 ≥ 3 => 4x ≥ 2 => x ≥ 0.5.
Correct Answer:
A
— x ≥ 0.5
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Q. Solve the inequality: 6 - x ≤ 2.
-
A.
x ≥ 4
-
B.
x ≤ 4
-
C.
x ≥ 6
-
D.
x ≤ 6
Solution
6 - x ≤ 2 => -x ≤ -4 => x ≥ 4.
Correct Answer:
B
— x ≤ 4
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Q. Solve the system: 6x + 5y = 30 and 4x - 3y = 6. What is the value of x?
Solution
From the first equation, 5y = 30 - 6x, so y = (30 - 6x)/5. Substituting into the second gives 4x - 3(30 - 6x)/5 = 6. Solving leads to x = 2.
Correct Answer:
B
— 2
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Q. Solve the system: 6x + 5y = 45 and 4x - 3y = 7. What is the value of y?
Solution
From the first equation, y = (45 - 6x)/5. Substituting into the second gives 4x - 3((45 - 6x)/5) = 7. Solving leads to y = 5.
Correct Answer:
A
— 5
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Q. Some birds can fly. All sparrows are birds. Therefore, some sparrows can fly. Is this conclusion valid? (2023)
-
A.
Yes
-
B.
No
-
C.
Only if all birds can fly
-
D.
Only if some birds are sparrows
Solution
The conclusion is valid. Since all sparrows are birds and some birds can fly, it follows that some sparrows can fly.
Correct Answer:
A
— Yes
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Q. Some cars are red. All red things are fast. Therefore, some cars are fast. (2023)
-
A.
True
-
B.
False
-
C.
Cannot be determined
-
D.
None of the above
Solution
The conclusion logically follows from the premises.
Correct Answer:
A
— True
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Q. Some cars are red. All red things are fast. Therefore, some cars are fast. Is this conclusion valid? (2023)
-
A.
Yes
-
B.
No
-
C.
Only if all cars are red
-
D.
Only if some fast things are cars
Solution
The conclusion is valid. If some cars are red and all red things are fast, then it follows that some cars are fast.
Correct Answer:
A
— Yes
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Q. Some fruits are apples. All apples are sweet. Therefore, some fruits are sweet. (2023)
-
A.
True
-
B.
False
-
C.
Cannot be determined
-
D.
None of the above
Solution
The conclusion logically follows from the premises.
Correct Answer:
A
— True
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