Transcript Graphing Solutions on a Number Line

Solving and
Graphing
Inequalities on
a Number Line
Think About how we Solve Equations
y+10 =16
What operation Is being done in this equation?
Addition
What is the inverse operation for addition?
Subtraction
y+10 =16
-10 -10
y=6
y+ 10 = 16
(6)+10 = 16
16 = 16
Now Solve the equation using inverse operations
Hold up – Check your work!
We Solve Inequalities the same way!
y+10 < 16
What operation Is being done in this inequality?
Addition
What is the inverse operation for addition?
Subtraction
y+10 < 16
-10 -10
y<6
y+ 10 < 16
(6)+10 < 16
16 = 16
Now Solve the equation using inverse operations
Hold up – Check your work!
Check an inequality
the same way you do
an equation, but the
values that make the
inequality will be more
than one.
The solutions for these two problems mean
different things!
y+10 = 16
Y=6
y+10 < 16
Y<6
For the equation: Y can only be equal to 6! There
is not another number that will make this
equation true!
For the inequality: Y can be more than one value,
but the value must be less than 6.
Graph the Solution
y=6
Use your manipulative to graph the solution on your
table number line
-∞
What is a lower value?
What is a larger value?
What are the possible values for y?
∞
Graph the Solution y < 6
Use your manipulative to graph the solution on your
table number line
-∞
What is a lower value?
What is a larger value?
What are the possible values for y?
∞
WhooHoooo!!!
You just
graphed
the solution
to an algebraic
Inequality.
Open Circle and Closed Circle
• Open Circle is used when the solution is not
included.
X<5
• Closed Circle is used when the solution is
included.
N > 3.5
• Shading to the left means solution includes
values lower than the solution.
• Shading to the right means solution include
values that are greater than the solution.
Graphing solutions on your own
• You don’t have to create an entire number
line each time you graph a solution
BUT
• You must always include:
– the solution
– lower value
– higher value
Solve and graph the solution for 5f>75
5f>75
What operation is being done in the inequality?
Multiplication
What is the inverse operation for multiplication?
Division
5f > 75
5 5
f > 15
Solve the inequality using inverse operations
5f>75
5(15) >75
75>75
Check your work!!
Graph the solution f > 15
Start with a blank number line
-∞
∞
Place your solution in the middle on the graph
-∞
∞
15
Place a lower value and a higher value on the graph
-∞
∞
14
15
16
Graph the solution f > 15
Since the inequality is greater than or equal, you will
include 15 in the graph. This means the circle will
be closed. You then shade the line to the right of
15 because these values are greater!
-∞
∞
14
15
16
You Try
Solve each inequality and graph the solution on a number line
1.
x <3
27
80
2. 6m > 162
3. b + 2 > 5
4. 2.75 + y < 16.5
5. .5t = 20.85
26
81
82
27
28
2
3
4
13
13.75 14
15
41
41.7
42
You Try
Solve each inequality and graph the solution on a number line
6.
x ≠3
27
80
81
82