Exploring Absolute Value Inequalities

The video tutorial covers absolute value inequalities, combining knowledge of compound inequalities and absolute value equations. It explains how to interpret and solve inequalities where the absolute value is less than or greater than a number, using 'and' and 'or' statements. The tutorial includes examples and graphing techniques to illustrate these concepts, emphasizing the importance of understanding the distance from zero and how it affects the solution set.

What are the two numbers that are exactly eight units away from zero?

• -8 and 8

• -6 and 6

• -4 and 4

• -2 and 2

If the distance from zero is less than eight, which of the following numbers is included in the solution?

• 9

• 8

• 7

• 10

What does the absolute value inequality |x| ≤ 2 represent on a number line?

• All numbers less than -2

• All numbers between -2 and 2, inclusive

• All numbers except 2 and -2

• All numbers greater than 2

Which of the following is true for the inequality |x| > 2?

• x is exactly 2

• x is between -2 and 2

• x is greater than 2 or less than -2

• x is exactly -2

When solving the inequality |x - 4| < 3, what is the first step?

• Divide by 3

• Add 4 to both sides

• Subtract 4 from both sides

• Multiply by 3

In the inequality |x - 4| < 3, what does the solution represent on a number line?

• All numbers between 1 and 7

• All numbers except 1 and 7

• All numbers greater than 7

• All numbers less than 1

When solving |x - 4| < 3, what is the final solution for x?

• x > 1 and x < 7

• x < 1 or x > 7

• x < 1 and x > 7

• 1 < x < 7

For the inequality |x + 2| > 9, what is the correct way to split it into two inequalities?

• x + 2 < 9 and x + 2 > -9

• x + 2 < -9 and x + 2 > 9

• x + 2 > 9 and x + 2 < -9

• x + 2 > 9 and x + 2 < 9

What is the solution to the inequality |x + 2| > 9?

• x > 7 or x < -7

• x > 11 or x < -11

• x > 7 or x < -11

• x > 11 or x < -7

In the inequality |x + 2| > 9, what does the solution represent on a number line?

• All numbers between -7 and 11

• All numbers except 7 and -11

• All numbers greater than 7 and less than -11

• All numbers greater than 11 and less than -7