# 3.1 Inequalities and Their Graphs

```3.1 Inequalities and Their
Graphs
Objective: SWBAT graph and determining
solutions of inequalities.
Mini Quiz 20
1. Express in miles per hour: 1 mi in 3 min
2. Fresh Flowers sells six roses for \$7.50. Find
the unit rate.
3. In converting rates, how do you set it up?
Quick Review
1. Name each inequality
&lt;
&gt;
Less Than
Greater Than
≤
Less Than
2. Fill in the correct inequality or equal to
&lt; 7
&gt; -3
a. 5 __
b. 0 __
&lt; -1
&lt; -0.01
c. -4 __
d. -0.1 __
3.Graph each number on the number line:
a. 0
b. 4
c. -2
0
≥
Greater Than
or equal to
Inequality Symbols
Symbol
Vocabulary
Graphed

Less Than


Greater Than
Less Than or Equal To

Greater Than or Equal To
OPEN
CLOSE
Reminder:
• “Less Than” has a L in italics (that’s tripping), which
looks like this &lt;
• The “Equal To” part fills in the dot…
Open or Solid?
Tell whether the following is an open dot or
close dot:
OPEN
1. x &gt; 7
CLOSE
2. x - 1 ≤ 23
OPEN
3. 5y &lt; -3
OPEN
4. -2x + 3 &gt; -5
CLOSE
5. -8 ≥ -y – 4
Graphing Inequalities
6. Graph n &gt; -2
7. Graph 4 ≤ m
8. Graph a &lt; 1
9. Graph y ≥ -3
0
0
0
0
Writing an Inequality
Write an inequality for each graph
10.
0
x&gt;2
11.
0
x≤0
12.
0
x≥1
13.
0
x &lt; -3
Mental Math
14. Is each number a solution of x ≤ 7?
a. 9
No
b. 14
Yes
2
15. Is each number a solution of x &gt; -4.1?
a. -5
No
b. -4.1
No
c. 8
Yes
d. 0
Yes
Identifying Solutions by Evaluating
16. Is each number a solution of 2 – 5x &gt; 13?
a. -4
Yes
b. 3
No
17. Is each number a solution of 6x – 3 &gt; 10?
a. 1
No
b. 2
No
c. 3
Yes
d. 4
Yes
Wrap Up

Inequalities





less than
greater than
less than or equal to
greater than or equal to
Graphing Inequalities



&lt;
&gt;
≤
≥
Open or Close