Chapter 4
Inequalities
4.1 Inequalities and Their Graphs
An inequality is a statement that two quantities
are not equal. The quantities are compared by
using the following signs:
<
A<B
A is less
than B.
≤
≥
A>B
A≤B
A≥B
A is greater
than B.
A is less
than or
equal to B.
>
A is greater
than or
equal to B.
.
Ex 1: Determine whether the given
number is a solution of the inequality of
x >4
a.) 4
4>4
False
c.) -4
-4>4
False
b.) 0
0>4
False
d.) 6
6>4
True
Graph the Inequality on the # line
1. Draw number line. Label zero and the
number where your arrow starts
2. Put a circle on the number.
Open Circle if < or >.
Solid Circle if “or equal to” ≤or≥.
3. Draw your solution graph line in the same
direction as the inequality IF the “x” is on left.
Ex 2: Graph the solution of
x > -2
-6
-4
-2
0
2
4
6
Ex 3: Graph the solution of
x  -2
If you have ≤ or ≥ you draw a closed circle
-6
-4
-2
0
2
4
6
Hint: When graphing make sure
your variable is on the left side
5<x
To make sure the graph is correct switch the variable
and number and flip the inequality.
x>5
Now graph it
-6
-4
-2
0
2
Ex 4: This is the graph of:
 -2
x > -2
x  -2
x < -2
1) x
2)
3)
4)
4
6
-6
-4
-2
0
2
Ex 5: This is the graph of:
1
x > -1
x  -1
x>1
1) x
2)
3)
4)
4
6
4.2
The Addition Property of
Inequalities
Addition Property of Inequalities
If a < b, then
a+c<b+c
The same is true for >,  , and

Ex 6: Solve for “x”and graph:
x-3>4
+3
+3
X>7
-8
-4
0
4
8
Ex 7: Solve for “x” and graph:
8z + 6 – 7z  16
Z + 6  16
-6
-6
z  10
-8
-4
0
4
8
1
1
Ex 8: Solve: x  
3 4
4
3
x

12 12
3 4
x 
12 12
7
x
12
Ex 9: 5(y-2)-4(y-1)<0
Assignment:
Page 173 (4-18, 26-30) even
Page 178 (8-36) even