6.4  Absolute Value and Inequalities

Mrs. Agriesti's Algebra

Goal: To solve absolute value inequalities.

To solve an absolute value inequality you need to  transform it into a compound inequality.  To do that:

  1. Get the absolute value part alone on the left side.
  2. If the inequality is less than use "and".  If the inequality is greater than use "or".
  3. Solve the inequality (see 6.3 notes if you need help).



Remember It This Way:

Read "<" as LESS AND
Read ">" as GREAT OR


Don't Forget to switch the inequality symbol if you multiply or divide by a negative number.

Examples:  Solve each inequality. 

Ex 1:   

The absolute value part is already by itself.  The inequality is greater than so use GREAT OR.

Solve each inequality.

or

Ex 2:   

Again, the absolute value part is already by itself.  This time the inequality is less than so use LESS AND.

Solve the compound inequality.

Ex 3:   

The absolute value part is by itself and the inequality is less than.  (Use LESS AND.)

Solve the compound inequality.

Notice that this time we divided by a negative number so we had to switch the inequality.

We also had to rewrite the compound inequality so that the smaller number (2) was on the left.

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