Solving Inequalities with Absolute Value

StandardsM8A2. Student will understand and graph inequalities in one variable.b. Use the properties of inequality to solve inequalities.c. Graph the solution of an inequality on a number line.

EQ: How do I solve and graph an inequality that includes absolute value?

Things we already know about Inequalities!!

>, < on graph

=, ≤, ≥, on graph

• When dividing or multiplying by a NEGATIVE number, we reverse the inequality symbol!!

Steps for Solving Inequalities with Absolute Values

1. Make sure Absolute Value is isolated! (Are there numbers not in the absolute value symbol?)

**Don’t forget when dividing or multiplying by negative number, reverse

inequality symbol**2. Write 2 Inequalities:

A. One inequality has EXACT inequality = positive answer

B. One inequality has REVERSE inequality = negative answer

3. Solve Inequalities following inequality rules!!4. Graph on number line using inequality rules!!

Let’s Goooooooooooooo!!!1. |n + 2| < 2

•Graph your solution.

2. |-6 + n| > 12

•Graph your solution.

3. | 3x | + 4 < 34

•Graph your solution.

•Graph your solution.

4. 37

x

5. | -8x – 10 | < 58

•Graph your solution.