Mastering Inequalities

Answer explanation

To solve the inequality 4x + 7 < 3x + 10, subtract 3x from both sides to get x + 7 < 10. Then, subtract 7 from both sides to find x < 3. Thus, the correct answer is x < 3.

Answer explanation

To solve the compound inequality -3 < x + 2 ≤ 5, subtract 2 from all parts: -5 < x ≤ 3. This matches the correct choice: -5 < x ≤ 3.

Answer explanation

To solve the inequality x - 5 > 2x - 3, first rearrange it to x < 8. Thus, the correct choice is x < 8.

What is the solution set for the inequality x^2 - 5x + 6 < 0?

• (1, 2)

• (2, 3)

• (3, 4)

• (-1, 0)

On a number line, where would you shade for the solution of x^2 + 3x < 10?

• Shade the interval (-5, 2) on the number line.

• Shade the interval (-10, -5) on the number line.

• Shade the interval (-3, 0) on the number line.

• Shade the interval (2, 5) on the number line.

Determine the intervals where the inequality x^2 - 2x - 3 ≤ 0 holds true.

• [0, 2]

• [3, 5]

• [-2, 0]

• [-1, 3]

Using a number line, represent the solution set for the inequality x^2 - 1 ≥ 0.

• (-∞, 1) ∪ (1, ∞)

• The solution set is represented on the number line as: (-∞, -1] ∪ [1, ∞).

• [-1, 1]

• [-1, ∞)

What intervals should be tested for the inequality x^2 + 2x - 8 < 0?

• (-6, -2)

• (0, 4)

• (-5, -3)

• (-4, 2)

Interpret the solution set of the inequality x^2 - 6x + 8 > 0 in interval notation.

• (-∞, 4)

• (-∞, 2) ∪ (4, ∞)

• (2, ∞)

• (2, 4)

How would you graph the solution set of the inequality x^2 + x - 12 > 0 on a number line?

• The solution set is represented by the intervals (-∞, 3) and (-4, ∞) on a number line.

• The solution set is represented by the intervals (-4, 3) on a number line.

• The solution set is represented by the intervals (-∞, -4) and (3, ∞) on a number line.

• The solution set is represented by the intervals (3, -4) on a number line.