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. The argument of the complex number z = -1 - i is?
-
A.
-3π/4
-
B.
3π/4
-
C.
π/4
-
D.
-π/4
Solution
The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = -3π/4.
Correct Answer: A — -3π/4
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Q. The equation x^2 + 2x + 1 = 0 can be factored as:
-
A.
(x + 1)(x + 1)
-
B.
(x - 1)(x - 1)
-
C.
(x + 2)(x + 1)
-
D.
(x - 2)(x - 1)
Solution
This is a perfect square: (x + 1)^2 = 0.
Correct Answer: A — (x + 1)(x + 1)
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Q. The equation x^2 + 4x + 4 = 0 has:
-
A.
Two distinct roots
-
B.
One repeated root
-
C.
No real roots
-
D.
None of these
Solution
The discriminant is 0, indicating one repeated root.
Correct Answer: B — One repeated root
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Q. The equation x^2 - 2x + 1 = 0 has:
-
A.
Two distinct roots
-
B.
One repeated root
-
C.
No real roots
-
D.
Infinitely many roots
Solution
The discriminant is 0, indicating one repeated root.
Correct Answer: B — One repeated root
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Q. The equation x^2 - 6x + k = 0 has roots that are both positive. What is the range of k?
-
A.
k < 0
-
B.
k > 0
-
C.
k > 9
-
D.
k < 9
Solution
For both roots to be positive, k must be greater than the square of half the coefficient of x: k > (6/2)^2 = 9.
Correct Answer: C — k > 9
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Q. The product of the roots of the equation x^2 + 7x + 10 = 0 is:
Solution
The product of the roots is given by c/a = 10/1 = 10.
Correct Answer: A — 10
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Q. The product of the roots of the equation x^2 - 7x + k = 0 is 10. What is the value of k?
Solution
Using Vieta's formulas, the product of the roots is k = 10. Thus, k = 17.
Correct Answer: B — 17
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