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
Download Presentation The PPT/PDF document "Solving Inequalities Equations" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Solving Inequalities Equations Slide2Slide3
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
XSlide5Slide6
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
.