Solving Inequalities with 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. Make 2 Inequalities:1. One inequality has EXACT inequality = positive answer

2. One inequality has REVERSE inequality = negative answer

Steps for Solving Inequalities with Absolute Values

3. Solve Inequalities following inequality rules!!**Don’t forget when dividing or multiplying by negative number, reverse

inequality symbol**

4. Graph on number line using inequality rules!!• >, < : on graph

• =, ≤, ≥, : on graph

Let’s Goooooooooooooo!!!1. |n + 2| < 2 •Is the absolute value isolated?

• Write the 2 related inequalities.

•Solve each inequality.

•Graph your solution.

n + 2 < 2 n + 2 > -2

n + 2 > -2 - 2 -2n > -4

n + 2 < 2 -2 -2 n < 0

2. |-6 + n| > 12•Is the absolute value isolated?

•Write the 2 related inequalities.

•Solve each inequality.

•Graph your solution.

- 6 + n > 12-6 + n < -12

n < -6+6 + 6 +6 + 6

n > 18