Definitions of the Day (DODs)

4.8 – Compound Inequalities

• Compound Inequality

Definition: Compound Inequality – Two inequalities that are joined by the word and or the word or.

Notice! A solution of a compound inequality joined by and is any number that makes both inequalities true.

Graphing “or” Inequalities

0

Graph: 3 or 1x x

-3

0

Graph: 0 or 5x x

-1

5

Notice!! When Graphing an “or” Inequality

We end up with two separate graphs combined as

one

Notice!! When Graphing an “or” Inequality

We end up with two separate graphs combined as

one

Graphing “and” Inequalities

0

Graph: 2 3x

-2

0

Graph: 45 and 100x x

100

3

45

Notice!! When Graphing an ”and” inequality,

we end up with a Line Segment

Notice!! When Graphing an ”and” inequality,

we end up with a Line Segment

Simply use the 3 simple steps for equation solving success on both inequalities!!

Remember these?Steps for Solving Compound Inequalities

BEWARE!!! If you multiply or divide both sides by a negative number, you must “flip” the inequality sign.

SOLVE AND GRAPH EACH INEQUALITY

) 1 or 2 83

xa x

) 0 2 1 5b t

SOLVE AND GRAPH EACH INEQUALITY

) 3 2 and 3 12c x y

Your Turn!!

) 25 400 or 100 4a g g

1. Solve and Graph on a number line:

) 4 2 5b x

Sentence Frames

1. It is important to differentiate between open and closed dots on a number line because… ________________________________________________________________________________________

1. A solution to a compound inequality joined by and must do what to both inequalities?____________________ ___________________________________________