Algebra Study Resources for Competitive Exam Success

Algebra

Binomial theorem Complex numbers Determinants Inverse Trigonometric Functions Linear Inequalities Logarithms Matrices Permutations & combinations Quadratic equations Sequence & series Sets & Relations

Q. What is the real part of the complex number z = 5 - 6i?

A. 5
B. -6
C. 11
D. 1

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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Algebra

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