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 angle between the lines represented by the equation 2x^2 + 3xy + y^2 = 0 is:
-
A.
0 degrees
-
B.
45 degrees
-
C.
90 degrees
-
D.
60 degrees
Solution
Using the angle formula, we find the angle between the lines is 60 degrees.
Correct Answer: D — 60 degrees
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Q. The angle between the lines represented by the equation 3x^2 - 4xy + 2y^2 = 0 is:
-
A.
30 degrees
-
B.
45 degrees
-
C.
60 degrees
-
D.
90 degrees
Solution
Using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, we find that the angle is 60 degrees.
Correct Answer: C — 60 degrees
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Q. The area of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4) is:
Solution
Length = 5 - 1 = 4, Width = 4 - 1 = 3. Area = Length * Width = 4 * 3 = 12.
Correct Answer: B — 16
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Q. The area of triangle ABC is 24 cm², and the base BC = 8 cm. What is the height from A to BC?
-
A.
6 cm
-
B.
8 cm
-
C.
4 cm
-
D.
3 cm
Solution
Area = 1/2 * base * height => 24 = 1/2 * 8 * height => height = 6 cm.
Correct Answer: A — 6 cm
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Q. The area of triangle ABC is 30 square units, and the base BC is 10 units. What is the height from A to BC?
-
A.
3 units
-
B.
6 units
-
C.
5 units
-
D.
4 units
Solution
Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 6 units.
Correct Answer: B — 6 units
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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 average of five numbers is 18. If one number is excluded, the average becomes 16. What is the excluded number?
Solution
Total sum = 5 * 18 = 90. New sum = 4 * 16 = 64. Excluded number = 90 - 64 = 26.
Correct Answer: C — 24
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Q. The average of five numbers is 18. If one number is removed, the average becomes 16. What was the removed number?
Solution
Total of five numbers = 5 * 18 = 90. Total of four numbers = 4 * 16 = 64. Removed number = 90 - 64 = 26.
Correct Answer: C — 24
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Q. The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel is:
-
A.
h^2 = ab
-
B.
h^2 > ab
-
C.
h^2 < ab
-
D.
a + b = 0
Solution
The lines are parallel if h^2 = ab.
Correct Answer: A — h^2 = ab
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Q. The condition for the lines represented by the equation x^2 + 2xy + y^2 = 0 to be coincident is:
-
A.
Discriminant > 0
-
B.
Discriminant = 0
-
C.
Discriminant < 0
-
D.
None of the above
Solution
For the lines to be coincident, the discriminant must be equal to zero.
Correct Answer: B — Discriminant = 0
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Q. The condition for the lines represented by the equation x^2 + y^2 + 2xy = 0 to be coincident is:
-
A.
Discriminant = 0
-
B.
Discriminant > 0
-
C.
Discriminant < 0
-
D.
None of the above
Solution
For the lines to be coincident, the discriminant of the quadratic must be zero.
Correct Answer: A — Discriminant = 0
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Q. The condition for the lines represented by the equation x^2 + y^2 - 4x - 6y + 9 = 0 to be coincident is:
-
A.
Discriminant = 0
-
B.
Discriminant > 0
-
C.
Discriminant < 0
-
D.
None of the above
Solution
For the lines to be coincident, the discriminant of the quadratic must equal zero.
Correct Answer: A — Discriminant = 0
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