BIM ALG1 2.6 Solving Absolute Value Inequalities

BIM ALGEBRA 1 2.6 Solving Absolute Value Inequalities

Remember

1) Absolute Value cannot be negative!

2) There are always two statements!

Example 1:

|x+7|<2

What do we do?

x+7<2..........and ----------x+7>-2

Solve on your table.

x+7<2 and x+7>-2

x+7-7<2-7 and x+7-7>-2-7

x<-5 and x>-9

x<-5 and x>-9

This was originally a Less Than Problem or a Less AND Problem. The graph will be an AND graph.

0-----------0

-----|------------|----

-9 .............. -5

--

Ex 2: |2x-1|>5

What do we do with this problem?

|2x-1|>5

2x-1>5 ....................2x-1<-5

2x-1+1>5+1..............2x-1+1<-5+1

2x>6...........................2x<-4

2x/2>6/2....................2x<-4/2

x>3.................................x-2

This was originally a GreatOR Than Problem. The graph will be an OR graph.

<-----0***************0---->

-----|--------------|----

-2....................-3

Ex 3. |3x+7|<0

This is saying that the absolute value is negative which we know is not possible. NO SOLUTIONS

EX4. |3x+7|>0

All absolute value problems are greater than zero by definition.

Infinite Solutions

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