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. Solve the inequality -x/2 + 4 > 0. What is the solution set?

A. x < 8
B. x > 8
C. x ≤ 8
D. x ≥ 8

Solution

-x/2 + 4 > 0 => -x/2 > -4 => x < 8.

Correct Answer: B — x > 8

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Q. Solve the inequality -x/2 + 4 > 0. What is the solution?

A. x < 8
B. x > 8
C. x < -8
D. x > -8

Solution

-x/2 + 4 > 0 => -x/2 > -4 => x < 8.

Correct Answer: A — x < 8

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Q. Solve the inequality 2(x - 1) > 3. What is the solution?

A. x > 5/2
B. x < 5/2
C. x > 1/2
D. x < 1/2

Solution

2(x - 1) > 3 => x - 1 > 3/2 => x > 5/2.

Correct Answer: A — x > 5/2

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Q. Solve the inequality 2(x - 1) > 3x + 4. What is the solution?

A. x < -1
B. x > -1
C. x < 1
D. x > 1

Solution

2(x - 1) > 3x + 4 => 2x - 2 > 3x + 4 => -x > 6 => x < -6.

Correct Answer: A — x < -1

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Q. Solve the inequality 2x + 4 ≤ 10.

A. x ≤ 3
B. x < 3
C. x ≥ 3
D. x > 3

Solution

2x + 4 ≤ 10 => 2x ≤ 6 => x ≤ 3.

Correct Answer: A — x ≤ 3

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Q. Solve the inequality 2x - 1 ≥ 3. What is the solution set?

A. x < 2
B. x > 2
C. x ≤ 2
D. x ≥ 2

Solution

2x - 1 ≥ 3 => 2x ≥ 4 => x ≥ 2.

Correct Answer: D — x ≥ 2

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Q. Solve the inequality 2x - 3 < 5.

A. x < 4
B. x < 3
C. x > 4
D. x > 3

Solution

2x - 3 < 5 => 2x < 8 => x < 4.

Correct Answer: A — x < 4

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Q. Solve the inequality 2x - 3 < 5. What is the solution set?

A. x < 4
B. x > 4
C. x < 3
D. x > 3

Solution

2x - 3 < 5 => 2x < 8 => x < 4.

Correct Answer: A — x < 4

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Q. Solve the inequality 2x - 7 ≥ 3. What is the solution?

A. x < 5
B. x > 5
C. x ≤ 5
D. x ≥ 5

Solution

2x - 7 ≥ 3 => 2x ≥ 10 => x ≥ 5.

Correct Answer: D — x ≥ 5

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Q. Solve the inequality 3(x - 1) > 2(x + 2). What is the solution?

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: B — x > 5

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Q. Solve the inequality 3(x - 1) < 2(x + 2). What is the solution?

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. Solve the inequality 3x + 2 > 5x - 4. What is the solution?

A. x < 3
B. x > 3
C. x < 2
D. x > 2

Solution

3x + 2 > 5x - 4 => 2 > 2x => x < 1.

Correct Answer: B — x > 3

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Q. Solve the inequality 3x + 5 < 2x + 8.

A. x < 3
B. x > 3
C. x < 2
D. x > 2

Solution

3x + 5 < 2x + 8 => x < 3.

Correct Answer: A — x < 3

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Q. Solve the inequality 3x - 4 < 2x + 1.

A. x < 5
B. x > 5
C. x ≤ 5
D. x ≥ 5

Solution

3x - 4 < 2x + 1 => x < 5.

Correct Answer: A — x < 5

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Q. Solve the inequality 3x - 7 < 2x + 1.

A. x < 8
B. x > 8
C. x < 6
D. x > 6

Solution

3x - 7 < 2x + 1 => x < 8.

Correct Answer: C — x < 6

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Q. Solve the inequality 4 - 2x ≤ 10. What is the solution?

A. x ≥ -3
B. x ≤ -3
C. x > -3
D. x < -3

Solution

4 - 2x ≤ 10 => -2x ≤ 6 => x ≥ -3.

Correct Answer: A — x ≥ -3

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Q. Solve the inequality 4 - x > 2x + 1. What is the solution?

A. x < 1
B. x > 1
C. x < 2
D. x > 2

Solution

4 - x > 2x + 1 => 3 > 3x => x < 1.

Correct Answer: A — x < 1

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Q. Solve the inequality 4 - x ≤ 2.

A. x ≥ 2
B. x ≤ 2
C. x > 2
D. x < 2

Solution

4 - x ≤ 2 => -x ≤ -2 => x ≥ 2.

Correct Answer: B — x ≤ 2

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Q. Solve the inequality 4 - x ≤ 2x + 1. What is the solution?

A. x ≤ 1
B. x ≥ 1
C. x ≤ 2
D. x ≥ 2

Solution

4 - x ≤ 2x + 1 => 3 ≤ 3x => x ≥ 1.

Correct Answer: A — x ≤ 1

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Q. Solve the inequality 4x + 5 > 3x + 10. What is the solution?

A. x < 5
B. x > 5
C. x < 10
D. x > 10

Solution

4x + 5 > 3x + 10 => x > 5.

Correct Answer: B — x > 5

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Q. Solve the inequality 4x - 1 > 3x + 2. What is the solution?

A. x < 3
B. x > 3
C. x ≤ 3
D. x ≥ 3

Solution

4x - 1 > 3x + 2 => x > 3.

Correct Answer: B — x > 3

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Q. Solve 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. Solve the inequality 4x - 1 ≥ 3x + 2. What is the solution?

A. x ≥ 3
B. x ≤ 3
C. x ≥ 1
D. x ≤ 1

Solution

4x - 1 ≥ 3x + 2 => x ≥ 3.

Correct Answer: C — x ≥ 1

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Q. Solve the inequality 4x - 7 > 9.

A. x > 4
B. x < 4
C. x > 3
D. x < 3

Solution

4x - 7 > 9 => 4x > 16 => x > 4.

Correct Answer: C — x > 3

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Q. Solve the inequality 4x - 7 < 9.

A. x < 4
B. x < 3
C. x > 4
D. x > 3

Solution

4x - 7 < 9 => 4x < 16 => x < 4.

Correct Answer: B — x < 3

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Q. Solve the inequality 4x - 7 ≥ 9.

A. x ≥ 4
B. x ≤ 4
C. x > 4
D. x < 4

Solution

4x - 7 ≥ 9 => 4x ≥ 16 => x ≥ 4.

Correct Answer: A — x ≥ 4

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Q. Solve the inequality 5 - 2x > 1. What is the solution?

A. x < 2
B. x > 2
C. x ≤ 2
D. x ≥ 2

Solution

5 - 2x > 1 => -2x > -4 => x < 2.

Correct Answer: B — x > 2

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Q. Solve the inequality 5 - 2x > 3.

A. x < 1
B. x > 1
C. x < -1
D. x > -1

Solution

5 - 2x > 3 => -2x > -2 => x < 1.

Correct Answer: B — x > 1

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Q. Solve the inequality 5 - 2x ≤ 3. What is the solution?

A. x ≥ 1
B. x ≤ 1
C. x > 1
D. x < 1

Solution

5 - 2x ≤ 3 => -2x ≤ -2 => x ≥ 1.

Correct Answer: B — x ≤ 1

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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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Algebra

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