1. 2.1 Writing and Graphing Inequalities

2. Inequalities
Mathematical sentences containing <, >, < or >
< is less than
> is greater than
< is less than or equal to
> is greater than or equal to

3. Writing Inequalities Example 1
A number w minus 3.5 is less than or equal to -2.
3 is less than a number n plus 5.
Zero is greater than or equal to twice a number x plus one.
w – 3.5 < -2
3 < n + 5
0 > 2x + 1

4. You try! 1) A number b is fewer than 3.4.
2) -7/10 is at least twice a number k minus 4.
b < 3.4
-7/10 > 2k - 4

5. Example 2 Determine whether each number is a solution to x > 5.
5 > 5 Yes, 5 is a solution because is equal to 5
b.) -7
-7 > 5 No, -7 is not a solution because it is not greater than 5

6. You try!
Determine whether the given number is a solution to the inequality.
1.) x < 3 a.) b.) -5 c.) 3
2.) x > 6 a.) 6 b.) 0 c.) 25

7. Graphing Inequalities
A graph of an inequality with one variable is on a number line.
<,> are graphed using an open point since that number is not included as a solution.
<, > are graphed using a closed point since that number is included as a solution.

8. Example 3 Graph x < 2 on a number line.
The solutions of x < 2 are all number less than 2. They are shown by shading all numbers to the left of 2 on a number line.

9. Example 4 Graph x > -3 on a number line.
The solutions of x > -3 are -3 and all points to the right of -3.

10. You try!
Graph x < 8 on a number line.

11. Example 5
Write an inequality that represents the graph.
x > -3

12. You try!
Write an inequality that represents the graph.
x < 4