## Tutoring on Solving Absolute Value Inequalities

Learning Objectives:

#### Understand to Solve Absolute Value Inequalities.

Math Tutoring on Solving Absolute Value Inequalities

Absolute Value Inequalities can be rewritten as compound inequalities with "AND" or "OR." This means we will be looking for either the intersection or the union of two inequalities.

Absolute value inequalities fall into two basic categories:

1.         | x | < c   or   | x | ≤ c

2.         | x | ˃ c   or   | x | ≥ c

The solutions of | x | < c   or   | x | ≤ c are those values such that,

-c < x < c which means x ˃ -c AND  x < c

-c ≤ x ≤ c which means x ≥ -c AND  x ≤ c

The solutions of | x | ˃ c   or   | x | ≥ c are those values such that,

x ˃ c OR  x <- c

x ˃ c OR  x <- c

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Hook Questions:

1.    What are compound value inequalities?

2.    What are absolute value inequalities?

3.    What is the solution of  | x | ≥ c?

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