## Objective:

**To solve and graph compound inequalities.**

## Vocabulary:

**Absolute Value Inequality**- an inequality that contains an absolute value.**Conjunction**- a compound inequality whose solution meets*both*conditions simultaneously.- The solution can be written as a continuous statement such as a < x < b.
- It is an intersection or an '
*and*' set relationship.

**Disjunction**- a compound inequality whose solution meets*either*of two separate statements.- The solution is written as two separate statements such as x < a or x > b.
- It is a union or an '
*or*' set relationship.

## Notes:

Solving*absolute value inequalities:*

- Isolate the absolute value part (Get the absolute value part alone).
- Decide if the problem is a
*conjunction*or a*disjunction*- Conjunction - The form is like
*|x| < 7*- I call this a
*less and*problem (almost rhymes with 'less than'). - Write this problem as a long
*conjoined*problem*−7 < x < 7* - Solve the problem like you would a normal inequality.
- Remember that you have three sides - what you do to one side you do to all.

- I call this a
- Disjunction - The form is like
*|x| > 7*- I call this a
*great or*problem (almost rhymes with 'greater'). - Write this problem as two separate problems
*x > 7*and*x < −7* - Notice that the inequality symbol is
*switched*and the sign is changed to*negative*on the second problem.

- I call this a

- Conjunction - The form is like
- Solve your rewritten inequality or inequalities.

## Examples:

### Solve:

Solve each inequality.- |x + 9| > 13

- |3x − 15| < 12

- |10 − 4x| < 2