Exploring Absolute Value Inequalities

The video tutorial covers solving absolute value inequalities, starting with a review of notation and definitions. It explains how solutions can be expressed as compound inequalities and demonstrates this with examples. The tutorial also addresses special cases where solutions may be all real numbers or no solution at all, emphasizing the importance of understanding the nature of absolute values.

What is an absolute value inequality?

• An inequality with at least one absolute value expression

• An equation with no absolute value expression

• A compound inequality with no absolute value

• A linear equation

What does the solution set of |x| < 6 represent?

• No solution

• All real numbers whose distance from 0 is more than 6

• All real numbers whose distance from 0 is less than 6

• All real numbers

How is the solution set of |x| < 6 denoted?

• -6 < x < 6

• x = 6

• x < -6 or x > 6

• x = -6

What does the solution set of |x| > 6 represent?

• No solution

• All real numbers whose distance from 0 is less than 6

• All real numbers whose distance from 0 is more than 6

• All real numbers

How is the solution set of |x| > 6 denoted?

• x < -6 or x > 6

• x = -6

• -6 < x < 6

• x = 6

What is the solution to the inequality |x + 6| > -5?

• All real numbers

• No solution

• x = 6

• x = -6

How do you denote the solution set of |x - 5| ≤ 3?

• x < -3 or x > 3

• x = 5

• x = -5

• 2 ≤ x ≤ 8

What is the first step in solving the inequality |x - 5| ≤ 3?

• Add 5 to both sides

• Isolate the absolute value term

• Multiply both sides by 2

• Subtract 5 from both sides

What is the solution to the inequality -|2x - 3| + 4 > 0?

• All real numbers

• x = -3

• No solution

• x = 3

What does the solution set of |x + 6| > 1 represent?

• All real numbers whose distance from -6 is less than 1

• All real numbers whose distance from -6 is more than 1

• No solution

• All real numbers