Transcript Graphing Inequalities

Graphing Inequalities 2.8
> ,≤ , <, ≥
Equations vs. Inequalities
What is the difference in an equation and an
inequality?
We will look at a graph of each to see how each graph “explains”
this difference.
Equations vs. Inequalities
An equation has only one solution. This solution can be graphed.
n + 5 = 8
-5
-5
n = 3
0
1
2 3 4
5
A graph of this solution would look like this.
An inequality has a range of values. The solutions (right now)
are infinite. A graph of an inequality could look like this.
n>3
0
1
2 3 4
5
What Do the Symbols Mean?
Baby is smaller than the boy.
“less than”
≥
This baby is at least as big as this baby
…..maybe bigger
“greater than or equal to”
<
<
Boy is bigger than the baby.
“greater than”
≤
This baby is no bigger than this baby.
…..maybe smaller.
“less than or equal to”
Inequalities can have more than one
value that makes the statement true.
You see inequalities all the time. You just don’t
think of them as inequalities!
Speed limits?
Height
requirements?
Age limits?
What do they mean?
You are not to drive over 70 mph.
You must be 4 ft.
tall to ride.
Can you be taller
than 4 ft? Shorter
than 4 ft?
Can you drive less than 70? Can
you drive 70 mph?
S ≤ 70 mph
Your speed must be equal to or
less than 70 mph
h ≥ 4ft
Your height (h) must be equal to
or greater than 4 ft.
You can vote
when you are 18.
You can vote when
you are older, too.
v ≥ 18
Reading the Inequality
As we graph inequalities, learn to “read” the inequality
from the variable. This will help as we graph the
values.
a< 12 means the arrow will point to values less than 12.
So does this……. 12 > a.
a > -2 means the arrow will point to values greater than -2.
So does this……. -2 < a.
Each sign has a special graph.
≥ means greater than or equal to
≤ means less than or equal to
> means greater than
< means less than
Go back in your notes and make each circle
next to its appropriate sign.
Do you notice anything?????
Arrows are used in graphing.
Since inequalities show a range of values, an
arrow is used with the correct “dot” to show
the numbers in that range. Numbers that fit in
this range are solutions to the inequality.
Using our example of a height range: (not in notes)
n ≥ 4 ft.
1
2 3 4 5
6
Speed Limit Graph?
50
60
70
80
90
Since you can go = to 70 the equal bar will be included under the inequality sign.
Since you have to go less than this, the sign will be a less than or = to.
The arrow must point to the numbers that are less than seventy. The solid
circle shows us that 70 is part of the answer.
Using the Open Circle….
Some of our examples will not use a solid circle.
Here is an inequality that would use an open
circle:
You have to be older than 4 ½ years old to attend
school.
Your age can’t be 4 ½ . It must be more than 4 ½.
a 4
3
4
5
6
Let’s Try Some! It will make more
sense when you graph your own.
Step 1:
Where do
you start?
y<3
2
3
4
n > -1
-1
Step 2:
Open or
closed?
Step 3:
Right or
left arrow?
0
1
-6 ≤ g
-7
-6
-5
On Your Own…..p. 102
Step 1:
Where do
you start?
z < -2
-3
-2
-1
4 >t
Step 2:
Open or
closed?
3
4
a ≥ -5
-5
Step 3:
Right or
left arrow?
5
-4
-3
2
3
2≥ c
1
Identifying the Inequality
n ≤ -1
n>0
What inequalities are represented by these graphs?
1
2
-1
4
3
0
5
2≤ n
1
6
or
0 > n or
n≥ 2
n<0
5 ≥ n or n ≤ 5
Writing Inequalities to Describe Real
World Situations
The words at most means no more than…
So the amount can be equal to or less than….
Writing Inequalities
Use this same label on p. 103 to write an inequality for n,
the number of milligrams of sodium in this sodium-free food.
Words:
A serving of sodium-free food
Inequality
n <
5
has
less than
5mg
In Review………
Graph the solutions of each inequality on a number line.
n > -2
-3
-2
-1
w ≥ -5
-6
-5
-4
6
7
6 > y
5
In Review………
Write the inequality shown on each graph.
n ≥ -3
-3≤ n
n<3
3>n
-4
2
-3
3
-2
4
Write an inequality to show this situation:
No more than 50 students participated in the
survey.
n ≤ 50
In Review………
Write the inequality shown on each graph.
n ≥ -3
-3≤ n
n<3
3>n
-4
2
-3
3
-2
4
Write an inequality to show this situation:
No more than 50 students participated in the
survey.
n ≤ 50
The End