Q. What is the real part of the complex number z = 5 - 6i?
Solution
The real part of z = 5 - 6i is 5.
Correct Answer: A — 5
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Q. What is the real part of the complex number z = 5e^(iπ/3)?
-
A.
5/2
-
B.
5/√3
-
C.
5√3/2
-
D.
5
Solution
The real part is Re(z) = 5cos(π/3) = 5 * 1/2 = 5/2.
Correct Answer: A — 5/2
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Q. What is the solution for the inequality 4 - x < 2?
-
A.
x > 2
-
B.
x < 2
-
C.
x > 4
-
D.
x < 4
Solution
4 - x < 2 => -x < -2 => x > 2.
Correct Answer: D — x < 4
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Q. What is the solution for the inequality 4x + 1 < 3x + 5?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 3
-
D.
x > 3
Solution
4x + 1 < 3x + 5 => x < 4.
Correct Answer: A — x < 4
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Q. What is the solution for the inequality 4x - 1 < 3x + 2?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 1
-
D.
x > 1
Solution
4x - 1 < 3x + 2 => x < 3.
Correct Answer: A — x < 3
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Q. What is the solution for the inequality 6 - 2x ≥ 0?
-
A.
x ≤ 3
-
B.
x > 3
-
C.
x < 3
-
D.
x ≥ 3
Solution
6 - 2x ≥ 0 => -2x ≥ -6 => x ≤ 3.
Correct Answer: A — x ≤ 3
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Q. What is the solution for the inequality 7 - 4x < 3?
-
A.
x > 1
-
B.
x < 1
-
C.
x > -1
-
D.
x < -1
Solution
7 - 4x < 3 => -4x < -4 => x > 1.
Correct Answer: B — x < 1
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Q. What is the solution for the inequality 7x + 2 ≤ 5x + 10?
-
A.
x ≤ 4
-
B.
x ≥ 4
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
7x + 2 ≤ 5x + 10 => 2x ≤ 8 => x ≤ 4.
Correct Answer: A — x ≤ 4
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Q. What is the solution for the inequality 7x + 3 < 24?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 4
-
D.
x > 4
Solution
7x + 3 < 24 => 7x < 21 => x < 3.
Correct Answer: C — x < 4
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Q. What is the solution for the inequality 8 - 3x > 2?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
8 - 3x > 2 => -3x > -6 => x < 2.
Correct Answer: C — x < 3
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Q. What is the solution for the inequality: 2x + 5 > 3x - 1?
-
A.
x < 6
-
B.
x > 6
-
C.
x < 4
-
D.
x > 4
Solution
2x + 5 > 3x - 1 => 6 > x => x < 6.
Correct Answer: D — x > 4
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Q. What is the solution set for the inequality -x + 6 > 0?
-
A.
x < 6
-
B.
x > 6
-
C.
x < 0
-
D.
x > 0
Solution
-x + 6 > 0 => -x > -6 => x < 6.
Correct Answer: A — x < 6
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Q. What is the solution set for the inequality 4x + 1 < 9?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 1
-
D.
x > 1
Solution
4x + 1 < 9 => 4x < 8 => x < 2.
Correct Answer: A — x < 2
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Q. What is the solution set for the inequality 4x - 1 < 3x + 2?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 1
-
D.
x > 1
Solution
4x - 1 < 3x + 2 => x < 3.
Correct Answer: A — x < 3
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Q. What is the solution set for the inequality 5 - 2x < 1?
-
A.
x > 2
-
B.
x < 2
-
C.
x > 3
-
D.
x < 3
Solution
5 - 2x < 1 => -2x < -4 => x > 2.
Correct Answer: A — x > 2
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Q. What is the solution set for the inequality 6x - 4 < 2x + 8?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 2
-
D.
x > 2
Solution
6x - 4 < 2x + 8 => 4x < 12 => x < 3.
Correct Answer: B — x > 3
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Q. What is the solution set for the inequality 7 - 4x ≤ 3?
-
A.
x ≥ 1
-
B.
x ≤ 1
-
C.
x ≥ -1
-
D.
x ≤ -1
Solution
7 - 4x ≤ 3 => -4x ≤ -4 => x ≥ 1.
Correct Answer: B — x ≤ 1
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Q. What is the solution set for the inequality 7x - 5 > 2?
-
A.
x > 1
-
B.
x < 1
-
C.
x > 2
-
D.
x < 2
Solution
7x - 5 > 2 => 7x > 7 => x > 1.
Correct Answer: A — x > 1
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Q. What is the solution set for the inequality x/3 - 1 ≤ 2?
-
A.
x ≤ 9
-
B.
x ≥ 9
-
C.
x < 9
-
D.
x > 9
Solution
x/3 - 1 ≤ 2 => x/3 ≤ 3 => x ≤ 9
Correct Answer: A — x ≤ 9
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Q. What is the solution to the compound inequality 1 < 2x + 3 < 7?
-
A.
-1 < x < 2
-
B.
0 < x < 2
-
C.
1 < x < 2
-
D.
1 < x < 3
Solution
1 < 2x + 3 < 7 => -2 < 2x < 4 => -1 < x < 2.
Correct Answer: A — -1 < x < 2
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Q. What is the solution to the inequality -2x + 4 > 0?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
-2x + 4 > 0 => -2x > -4 => x < 2.
Correct Answer: B — x > 2
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Q. What is the solution to the inequality -2x + 5 > 1?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
-2x + 5 > 1 => -2x > -4 => x < 2.
Correct Answer: B — x > 2
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Q. What is the solution to the inequality 2x + 3 < 7?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
2x + 3 < 7 => 2x < 4 => x < 2.
Correct Answer: A — x < 2
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Q. What is the solution to the inequality 2x + 5 > 3x - 1?
-
A.
x < 6
-
B.
x > 6
-
C.
x < 4
-
D.
x > 4
Solution
2x + 5 > 3x - 1 => 6 > x => x < 6
Correct Answer: D — x > 4
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Q. What is the solution to the inequality 3(x - 1) < 2(x + 2)?
-
A.
x < 5
-
B.
x > 5
-
C.
x < 4
-
D.
x > 4
Solution
3(x - 1) < 2(x + 2) => 3x - 3 < 2x + 4 => x < 7.
Correct Answer: C — x < 4
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Q. What is the solution to the inequality 3x - 5 ≤ 4?
-
A.
x ≤ 3
-
B.
x ≥ 3
-
C.
x < 3
-
D.
x > 3
Solution
3x - 5 ≤ 4 => 3x ≤ 9 => x ≤ 3
Correct Answer: A — x ≤ 3
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Q. What is the solution to the inequality 4 - x < 2?
-
A.
x > 2
-
B.
x < 2
-
C.
x > 4
-
D.
x < 4
Solution
4 - x < 2 => -x < -2 => x > 2.
Correct Answer: D — x < 4
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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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