## Solving InequalitiesBy Lanie Mullen, LasANDRA COOK & SEYDOU gandega

Solving Inequalities 6.1 by Lanie Mullen

So first off why do we even solve inequalities?

We solve them to get whatever variable we have like X for example to get it on its own with the inequality sign. Also an inequality is a range of solutions and when you graph it you need to include all the points that work.

Example: x < 5

Graphing inequalities and multi step inequalities

Try these problems

Remember: < is not equal too but <= is equal

X>2

You should've gotten something like this because X is greater than 2

More practice problems

X>= 4

X<5

Now we're gonna try multi step Inequalities

M-8>3

Answer (see so simple)

Let's try another one!

-5(x-4)<=35

Solving Inequalities 6.2 by Lasandra Cook

Compound Inequalities

consists of 2 distinct quantities joined by the word “and” or “or"

For example

"And"

Contains the overlap of the graphs of the two inequalities

-2>x and x<0

-2>x<0

For example

"Or"

Contains each graph of the two inequalities

X< 3 or x> 5

Here try it yourself

-1<x and x<2

X<-3 or x<4

Now we are going to do solve and graph the solution

Make sure to graph it when your done!

Practice

N-5<-12 OR 6n >48

-5 -5 6n>48

N<-17 N>8

-3<x+5 OR. -3<x-4

-5. -5. +4. +4

-8<x 1<x

Solving Inequalities 6.3 by Seydou Gandega

Definition of absolute value

Absolute value is the distance from zero it's always positive it can never be negative

Examples of absolute value

|10|=10

True or false

|x|=15

What number can I sustitute to replace x that make the absolute value of x=15

Inequalities

#1 Is this true or false

> is this greater or less

Solving Inequalities 6.4 by Lanie Mullen

Linear inequalities and systems

System of linear inequalities are made up of two or more inequalities

For example

Another example of doing this is y<2x-3 & 2x+y>2

Then you graph it!

More examples

Y=my+b & y<= 1/2x +2 = y<-2x-3

Y>3x-2 & 2y-x<= 6

Y=mx+b & y=2/3x+3

Credits:

Created with images by red, white, and black eyes forever - "AEST" • (vincent desjardins) - "Chicago (ILL) Millennium Park, Crown Fountain, Jaume Plensa. 2004" • edenpictures - "People" • pan.li53 - "Make Your Own Graffi" • OchoCerditos - "graffitis"