# Fill in the blank with , or = to make each statement true. ```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:
&lt;
A&lt;B
A is less
than B.
≤
≥
A&gt;B
A≤B
A≥B
A is greater
than B.
A is less
than or
equal to B.
&gt;
A is greater
than or
equal to B.
.
Ex 1: Determine whether the given
number is a solution of the inequality of
x &gt;4
a.) 4
4&gt;4
False
c.) -4
-4&gt;4
False
b.) 0
0&gt;4
False
d.) 6
6&gt;4
True
Graph the Inequality on the # line
1. Draw number line. Label zero and the
2. Put a circle on the number.
Open Circle if &lt; or &gt;.
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 &gt; -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&lt;x
To make sure the graph is correct switch the variable
and number and flip the inequality.
x&gt;5
Now graph it
-6
-4
-2
0
2
Ex 4: This is the graph of:
 -2
x &gt; -2
x  -2
x &lt; -2
1) x
2)
3)
4)
4
6
-6
-4
-2
0
2
Ex 5: This is the graph of:
1
x &gt; -1
x  -1
x&gt;1
1) x
2)
3)
4)
4
6
4.2
Inequalities
If a &lt; b, then
a+c&lt;b+c
The same is true for &gt;,  , and

Ex 6: Solve for “x”and graph:
x-3&gt;4
+3
+3
X&gt;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)&lt;0
Assignment:
Page 173 (4-18, 26-30) even
Page 178 (8-36) even
```