Understanding Absolute Values and Inequalities

The video tutorial explains how to solve inequalities involving absolute values. It covers three different inequalities, demonstrating how to determine which values of x satisfy each inequality. The first inequality is |x| < 7, where x values like -2 and 6 satisfy it. The second inequality is |x| > 5, with x = -9 as a solution. The third inequality, |x| > -16, is shown to be true for all x, as absolute values are always non-negative.

What is the main objective of the video tutorial?

• To practice graphing inequalities

• To learn about the history of absolute values

• To determine which x values satisfy given inequalities

• To solve equations involving absolute values

What is the absolute value of negative seven?

• Negative seven

• Zero

• Seven

• Fourteen

Which x value satisfies the inequality |x| < 7?

• x = -8

• x = 9

• x = -2

• x = 8

Which of the following is true for the inequality |x| < 7?

• x = 8 satisfies the inequality

• x = 6 satisfies the inequality

• x = 7 satisfies the inequality

• x = -8 satisfies the inequality

For the inequality |x| > 5, which x value is correct?

• x = -4

• x = 3

• x = -9

• x = 0

What is the absolute value of -9?

• 18

• 9

• 0

• -9

What is the result of |3| in the context of the inequality |x| > 5?

• 3 is not a valid input

• 3 is equal to 5

• 3 is less than 5

• 3 is greater than 5

Which x value does not satisfy the inequality |x| > 5?

• x = 3

• x = -9

• x = 6

• x = -6

Why is the inequality |x| > -16 true for all x?

• Because absolute values are always positive

• Because absolute values are always negative

• Because absolute values are always zero

• Because absolute values are always non-negative

What is the absolute value of 15?

• 0

• 30

• -15

• 15