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Solving Inequalities Equations Solving Inequalities Equations

Solving Inequalities Equations - PowerPoint Presentation

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Solving Inequalities Equations - PPT Presentation

If you read from left to right 10 is greater than 5 X If you read from right to left 5 is less than 10 X If you read from left to right 5 is less than ID: 547611

side inequality solving equations inequality side equations solving inequalities compound number circle line equal solve equation divide drop lefts include work graph

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Slide1

Solving Inequalities Equations Slide2
Slide3

If you read from left to right

10

“is greater than “

5

XSlide4

If you read from right to left

5

“is less than “

10

XSlide5
Slide6

If you read from left to right

5

“is less than “

10

XSlide7

If you read from right to left

10

“is greater than“

10

XSlide8

Number line

.

X is equal to

7

Therefore you include the

7

with a dotted

cirle

.Slide9

Number line

.Slide10

Number line

.

X is equal to

-3

Therefore you include the

-3

with a dotted circle.Slide11

Number line

.Slide12

Number line

.

X is greater equal to

-2

Therefore you include the

-2

with a dotted circle.

You draw and

arrow

to the right Slide13

Number line

.Slide14

Number line

O

X is greater than

2

Therefore you do not include the

2

with an open circle.

You draw and

arrow

to the right Slide15

Number line

OSlide16

Number line

.

X is less than equal to

-6

Therefore you include the

-6

with an dotted closed circle

You draw and

arrow

to the left Slide17

Number line

.Slide18

Number line

O

X is less than

-6

Therefore you do not include the

-6

with an open circle

You draw and

arrow

to the left Slide19

Number line

OSlide20

Inequality Symbols

> Greater Than

>

Greater Than Equal

T

o

<

Less Than

<

Less Than Equal to

Open Circle indicates Not Equal

Closed Circle indicates Equal To

Open Circle indicates Not Equal

Closed Circle indicates Equal To Slide21

X + 5 =

13

What Side of the equation you are going to work with ?

The Rights side

The lefts side

Solving Inequality Equations Slide22

X + 5

>

13

What Side of the equation you are going to work with ?

The Rights side

The lefts side

Solving Inequality Equations Slide23

X + 5

>

13

What Side of the equation you are going to work with ?

…Because that’s where the variable is.

The lefts side

Solving Inequality Equations Slide24

X + 5

>

13

You subtract

– 5 in both side of the equatiion

.

-5

-5

_________

Solving Inequality Equations Slide25

X + 5

>

13

- 5 - 5

_________

Cancel

5

X

8

You drop down the

X

.

And then subtract

13

– 5 =

8.

Drop down

>

sign.

>

Solving Inequality Equations Slide26

X + 5

>

13

- 5 - 5

_________

X

8

>

.

X is

Greater

than equal to

8

Therefore

you

include

the

8

with

a closed

circle

You draw and

arrow

to the

right

Solving Inequality Equations Slide27

2x

<

18

What Side of the equation you are going to work with ?

The Rights side

The lefts side

Solving Inequality Equations Slide28

2x

<

18

What Side of the equation you are going to work with ?

…Because that’s where the variable is.

The lefts side

Solving Inequality Equations Slide29

2x

<

18

___

__

2

2

You divide by

2 in both side.

_________

1

x

<

9

Now

2

divide

2 gives you 1 x.

You drop down “

<

Now add

18 2 gives you 9.

÷

Solving Inequality Equations Slide30

2x

<

18

___

__

2

2

_________

1

x

<

9

O

Solving Inequality Equations

X is

Less than

9

Therefore

you

do not include

the

9

with

an opened circle

You draw and

arrow

to the l

eft Slide31

x

4

>

- 2

What Side of the equation you are going to work with ?

The Rights side

The lefts side

Solving Inequality Equations Slide32

x

4

>

- 2

What Side of the equation you are going to work with ?

…Because that’s where the variable is.

The lefts side

Solving Inequality Equations Slide33

x

4

>

- 2

You multiply by

4

in both side.

4

4

Now

4

divide

4

gives you 1X.

___________

1

x

You drop down

>

>

Now

-2

multiply by

4

equals

-8.

-8

Solving Inequality Equations Slide34

x

4

>

- 2

4

4

___________

1

x

>

-8

.

Solving Inequality Equations

X is

Greater equal to

-8

Therefore

you

do include

the

-8

with

an closed circle

You draw and

arrow

to the

right Slide35

In Inequalities there are two cases you Need to Flip The SignSlide36

When you multiply or divide by a negative number

Flip the Sigh of Inequality Slide37

- 5X

- 3

>

12

What Side of the equation you are going to work with ?

The Rights side

The lefts side

Solving Inequality Equations Slide38

What Side of the equation you are going to work with ?

…Because that’s where the variable is.

- 5X

- 3

>

12

The lefts side

Solving Inequality Equations Slide39

You add by

3 in both side.

+

3

+

3

You drop down

-5x

-5X

Cancel

3

You drop down

>

>

Now

12

plus

3

gives you

15.

15

___________

- 5X

- 3

>

12

Solving Inequality Equations Slide40

+

3

+

3

-5X

>

15

___________

- 5X

- 3 >

12

Now divide by

-5

in both sides

Now

-5

divide

-5

gives you 1X.

You drop down “

>

“ and flip the sign

__

-5

__

-5

___________

1

x

<

Now

15

divide by

5

equals

-3

- 3

Solving Inequality Equations Slide41

+

3

+

3

-5X

>

15

___________

- 5X

- 3 >

12

__

-5

__

-5

___________

1

x

<

- 3

O

Solving Inequality Equations Slide42

Second Case when you flip the Inequalities Sign

X

When the variable is in the right side of the equation

Change it to the left side.Slide43

When the variable is in the right side of the equation

Second Case when you flip the Inequalities Sign

And

Flip

the sign

X

Change it to the left side.Slide44

- 44

<

- 8

+

6X

You add

+ 8 in both side

.

+8

+8

___________

Now

-44

plus

8

gives you

-36.

36

You drop down “

<

<

Cancel

8

Now You drop down

6x

6X

Solving Inequality Equations Slide45

- 44

<

- 8

+

6X

+8

+8

___________

36

<

6X

Now divide by

6

in both sides

__

__

6

6

Now

36

divide

6 gives you

6

.

Drop

<

and

6

divide

6

gives you 1X.

___________

6

<

X

1

Solving Inequality Equations Slide46

- 44

<

- 8

+

6X

+8

+8

___________

36

<

6X

__

__

6

6

___________

6

<

X

1

Solving Inequality Equations Slide47

- 44

<

- 8

+

6X

+8

+8

___________

36

<

6X

__

__

6

6

___________

6

<

X

Solving Inequality Equations Slide48

- 44

<

- 8

+

6X

+8

+8

___________

36

<

6X

__

__

6

6

___________

6

>

X

Solving Inequality Equations Slide49

- 44

<

- 8

+

6X

+8

+8

___________

36

<

6X

__

__

6

6

___________

6

>

X

.

Solving Inequality Equations Slide50

Compound

Inequalities

A compound inequality consists of two inequalities that are joined together by the word "

and

" or the word "

or

".

x > -3 and x < 5Slide51

Compound

Inequalities

A compound inequality consists of two inequalities that are joined together by the word "

and

" or the word "

or

".

x > -3 and x < 5Slide52

Compound

Inequalities

x > -3 and x < 5Slide53

Compound

Inequalities

x > -3 and x < 5

O

O

X>-3

X<5Slide54

Compound

Inequalities

x > -3 and x < 5

O

O

O

O

X>-3

X<5Slide55

Compound

Inequalities

x > -3 and x < 5

O

O

O

O

X<5

X>-3Slide56

Compound

Inequalities

x > -3 and x < 5

O

OSlide57

Compound

Inequalities

x < -3 or x

>

5

O

X<-3

X

>

5

O

NO SOLUTIONSlide58

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10< 2x + 8

<

16

Solve the Two Inequalities Independently Slide59

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10<

2x + 8

<

16

Solve the Two Inequalities Independently 10< 2x + 8 2x + 8< 16

andSlide60

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10<

2x + 8

<

16

10< 2x + 8 2x + 8< 16

andSlide61

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10<

2x + 8

<

16

10< 2x + 8 2x + 8< 16and

-8 - 8

______

2

<

2x

__

2

__

2

______

1

<

x

x

1

>

-8 -8

______

______

2x

<

8

__

2

__

2

x

<

4Slide62

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10<

2x + 8

<

16

10< 2x + 8 2x + 8< 16and

-8 - 8

______

2

<

2x

__

2

__

2

______

1

<

x

x

1

>

-8 -8

______

______

2x

<

8

__

2

__

2

x

<

4Slide63

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10<

2x + 8

< 16

x 1 > x

<

4Slide64

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10<

2x + 8

< 16

OSlide65

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10<

2x + 8

< 16

O

O

.Slide66

Compound

Inequalities - Example 1

Solve and Graph the following Inequality

10<

2x + 8

< 16

O

O

.