Solving Absolute Value Disjunction Inequalities

The video tutorial explains how to solve absolute value disjunction inequalities by writing two separate inequalities. It covers the concept of absolute value as a distance from zero and the need to solve equations twice, once for positive and once for negative values. The tutorial also discusses compound inequalities, their types, and how to determine if a solution set is conjoint or disjoint. A practical example using a number line is provided, followed by a real-world application involving the acceptable weight range of a cereal box. The video concludes with a verification of solutions using test values.

What does the absolute value of a number represent?

• The distance from zero on the number line

• The negative of the number

• The number itself

• The square of the number

When solving the inequality |2x + 3| > 9, what are the two inequalities you need to solve?

• 2x + 3 > 9 and 2x + 3 < -9

• 2x + 3 > 9 and 2x + 3 < 0

• 2x + 3 > 9 and 2x + 3 < -9

• 2x + 3 > 9 and 2x + 3 < 9

How do you represent the solution x < -6 on a number line?

• An open circle over -6 with an arrow to the right

• A closed circle over -6 with an arrow to the left

• An open circle over -6 with an arrow to the left

• A closed circle over -6 with an arrow to the right

In the cereal box problem, what inequality represents weights that are not acceptable?

• |x - 18| ≤ 0.4

• |x - 18| = 0.4

• |x - 18| < 0.4

• |x - 18| > 0.4

What is the acceptable weight range for the cereal box?

• Between 17.6 ounces and 18.4 ounces

• Less than 17.6 ounces or more than 18.4 ounces

• Less than 18 ounces

• Exactly 18 ounces