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Inequalities

Description: Test your understanding of Inequalities, a fundamental concept in Algebra.
Number of Questions: 15
Created by:
Tags: inequalities algebra mathematics
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Solve the inequality: (x + 5 > 10)

  1. (x > 5)

  2. (x < 5)

  3. (x > 15)

  4. (x < 15)

Show answer
Correct Option: A
Explanation:

Subtract 5 from both sides: (x + 5 - 5 > 10 - 5). This simplifies to (x > 5).

Which inequality represents the statement "A number (x) is less than or equal to 12"?

  1. (x < 12)

  2. (x > 12)

  3. (x \leq 12)

  4. (x \geq 12)

Show answer
Correct Option: C
Explanation:

The symbol (\leq) means "less than or equal to".

Solve the inequality: (2x - 3 < 9)

  1. (x < 6)

  2. (x > 6)

  3. (x < 3)

  4. (x > 3)

Show answer
Correct Option: A
Explanation:

Add 3 to both sides: (2x - 3 + 3 < 9 + 3). This simplifies to (2x < 12). Divide both sides by 2: (\frac{2x}{2} < \frac{12}{2}). This simplifies to (x < 6).

Which of the following inequalities is equivalent to (3x + 5 \geq 17)?

  1. (3x \geq 12)

  2. (3x \leq 12)

  3. (x \geq 4)

  4. (x \leq 4)

Show answer
Correct Option: C
Explanation:

Subtract 5 from both sides: (3x + 5 - 5 \geq 17 - 5). This simplifies to (3x \geq 12). Divide both sides by 3: (\frac{3x}{3} \geq \frac{12}{3}). This simplifies to (x \geq 4).

Solve the inequality: (-2(x + 4) > 10)

  1. (x > -9)

  2. (x < -9)

  3. (x > -3)

  4. (x < -3)

Show answer
Correct Option: B
Explanation:

Distribute the -2: (-2x - 8 > 10). Add 8 to both sides: (-2x - 8 + 8 > 10 + 8). This simplifies to (-2x > 18). Divide both sides by -2, reversing the inequality: (\frac{-2x}{-2} < \frac{18}{-2}). This simplifies to (x < -9).

Which inequality represents the statement "The sum of (x) and 7 is greater than or equal to 15"?

  1. (x + 7 > 15)

  2. (x + 7 < 15)

  3. (x - 7 \geq 15)

  4. (x - 7 \leq 15)

Show answer
Correct Option:
Explanation:

The symbol (\geq) means "greater than or equal to".

Solve the inequality: (\frac{x}{2} + 3 \leq 7)

  1. (x \leq 8)

  2. (x \geq 8)

  3. (x \leq 4)

  4. (x \geq 4)

Show answer
Correct Option: A
Explanation:

Subtract 3 from both sides: (\frac{x}{2} + 3 - 3 \leq 7 - 3). This simplifies to (\frac{x}{2} \leq 4). Multiply both sides by 2: (2 \cdot \frac{x}{2} \leq 2 \cdot 4). This simplifies to (x \leq 8).

Which of the following inequalities is equivalent to (2 - 3x < 11)?

  1. (3x > -9)

  2. (3x < -9)

  3. (x > 4)

  4. (x < 4)

Show answer
Correct Option: C
Explanation:

Subtract 2 from both sides: (2 - 3x - 2 < 11 - 2). This simplifies to (-3x < 9). Divide both sides by -3, reversing the inequality: (\frac{-3x}{-3} > \frac{9}{-3}). This simplifies to (x > 4).

Solve the inequality: (4(2x - 1) \geq 20)

  1. (x \geq 3)

  2. (x \leq 3)

  3. (x \geq 5)

  4. (x \leq 5)

Show answer
Correct Option: C
Explanation:

Distribute the 4: (8x - 4 \geq 20). Add 4 to both sides: (8x - 4 + 4 \geq 20 + 4). This simplifies to (8x \geq 24). Divide both sides by 8: (\frac{8x}{8} \geq \frac{24}{8}). This simplifies to (x \geq 3).

Which inequality represents the statement "The difference between (x) and 10 is at most 5"?

  1. (x - 10 \leq 5)

  2. (x - 10 \geq 5)

  3. (10 - x \leq 5)

  4. (10 - x \geq 5)

Show answer
Correct Option: A
Explanation:

The phrase "at most" means "less than or equal to".

Solve the inequality: (\frac{3x + 2}{4} < 5)

  1. (x < 6)

  2. (x > 6)

  3. (x < 8)

  4. (x > 8)

Show answer
Correct Option: A
Explanation:

Multiply both sides by 4: (3x + 2 < 5 \cdot 4). This simplifies to (3x + 2 < 20). Subtract 2 from both sides: (3x + 2 - 2 < 20 - 2). This simplifies to (3x < 18). Divide both sides by 3: (\frac{3x}{3} < \frac{18}{3}). This simplifies to (x < 6).

Which of the following inequalities is equivalent to (5 - 2x \leq 1)?

  1. (2x \geq 4)

  2. (2x \leq 4)

  3. (x \geq 2)

  4. (x \leq 2)

Show answer
Correct Option: A
Explanation:

Subtract 5 from both sides: (5 - 2x - 5 \leq 1 - 5). This simplifies to (-2x \leq -4). Multiply both sides by -1, reversing the inequality: (-1 \cdot (-2x) \geq -1 \cdot (-4)). This simplifies to (2x \geq 4).

Solve the inequality: (2(x - 3) + 5 \geq 13)

  1. (x \geq 5)

  2. (x \leq 5)

  3. (x \geq 7)

  4. (x \leq 7)

Show answer
Correct Option: C
Explanation:

Distribute the 2: (2x - 6 + 5 \geq 13). Simplify: (2x - 1 \geq 13). Add 1 to both sides: (2x - 1 + 1 \geq 13 + 1). This simplifies to (2x \geq 14). Divide both sides by 2: (\frac{2x}{2} \geq \frac{14}{2}). This simplifies to (x \geq 7).

Which inequality represents the statement "Three times a number (x) is no more than 12"?

  1. (3x \leq 12)

  2. (3x \geq 12)

  3. (x \leq 4)

  4. (x \geq 4)

Show answer
Correct Option: A
Explanation:

The phrase "no more than" means "less than or equal to".

Solve the inequality: (\frac{2x + 1}{3} - 4 \leq 1)

  1. (x \leq 9)

  2. (x \geq 9)

  3. (x \leq 11)

  4. (x \geq 11)

Show answer
Correct Option: C
Explanation:

Add 4 to both sides: (\frac{2x + 1}{3} - 4 + 4 \leq 1 + 4). This simplifies to (\frac{2x + 1}{3} \leq 5). Multiply both sides by 3: (3 \cdot \frac{2x + 1}{3} \leq 3 \cdot 5). This simplifies to (2x + 1 \leq 15). Subtract 1 from both sides: (2x + 1 - 1 \leq 15 - 1). This simplifies to (2x \leq 14). Divide both sides by 2: (\frac{2x}{2} \leq \frac{14}{2}). This simplifies to (x \leq 7).

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