Understanding Absolute Value Inequalities

This video tutorial covers four basic absolute value inequalities, demonstrating how to graph the solution sets and express them using interval notation. It explains the concept of absolute value as a number's distance from zero and provides examples of inequalities with both open and closed intervals. The tutorial also includes advanced examples, emphasizing the importance of reversing inequality symbols when multiplying or dividing by negative numbers. The video concludes with a summary of key concepts and methods for solving absolute value inequalities.

What does the absolute value of a number represent?

• The number's distance from infinity

• The number's distance from ten

• The number's distance from one

• The number's distance from zero

How do you represent the solution set for |x| < 3 on a number line?

• Using closed points at 0 and 3

• Using open points at 0 and 3

• Using open points at -3 and 3

• Using closed points at -3 and 3

What type of interval is represented by |x| ≤ 6?

• Closed interval

• Open interval

• Half-open interval

• Infinite interval

Which notation is used to indicate that endpoints are included in an interval?

• Square brackets

• Braces

• Angle brackets

• Parentheses

What must you do to the inequality symbol when multiplying or dividing by a negative number?

• Reverse it

• Keep it the same

• Add one to it

• Subtract one from it

What is the solution set for -|x| ≥ -6?

• All numbers greater than 6

• All numbers less than 6

• All numbers between -6 and 6, inclusive

• All numbers between -6 and 6, exclusive

How do you solve the inequality 2|x| < 10?

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by 2

• Multiply both sides by 2

What is the solution set for 2|x| < 10?

• All numbers between -5 and 5, inclusive

• All numbers between -5 and 5, exclusive

• All numbers greater than 5

• All numbers less than 5

Which notation is used to indicate that endpoints are not included in an interval?

• Square brackets

• Angle brackets

• Braces

• Parentheses

What is the first step in solving the inequality 2|x| < 10?

• Add 10 to both sides

• Multiply both sides by 2

• Subtract 10 from both sides

• Divide both sides by 2