Understanding Absolute Value Inequalities

The video tutorial covers solving and graphing absolute value inequalities. It explains how to determine which values are in the solution set using graphical methods. The tutorial includes examples of graphing on a number line and discusses different ways to express intervals. It also addresses complex inequalities and emphasizes the importance of reversing inequality symbols when multiplying or dividing by negative numbers.

What does the absolute value of a number represent?

• The number's distance from zero

• The number's distance from one

• The number's distance from infinity

• The number's distance from negative one

Which of the following values is NOT in the solution set for |x| ≤ 7?

• 0

• -1

• 12

• 7

When solving -|x| > -2, what is the resulting inequality after reversing the inequality?

• |x| < 2

• |x| ≥ 2

• |x| ≤ 2

• |x| > 2

Which value is in the solution set for |x| < 2?

• 7

• 12

• 0

• -2

What happens to the inequality when both sides are multiplied by a negative number?

• The inequality disappears

• The inequality becomes an equation

• The inequality reverses

• The inequality remains the same

For the inequality |x| > 7, which value is included in the solution set?

• 0

• -1

• 12

• 7

What is the correct graph representation for |x| > 7?

• Closed interval between -7 and 7

• Open interval beyond -7 and 7

• Open interval between -7 and 7

• Closed interval beyond -7 and 7

What is the solution set for the inequality -|(-x)| ≤ 5?

• Only positive numbers

• Only negative numbers

• No real numbers

• All real numbers

Why is the solution set for -|(-x)| ≤ 5 all real numbers?

• Because absolute values are always non-negative

• Because it only includes positive numbers

• Because absolute values can be negative

• Because zero is included

Which of the following is true about absolute values?

• They are always non-negative

• They are always zero

• They can be negative

• They are always positive