The document provides instructions on: 1) The meanings of the inequality symbols <, >, ≤, ≥ and how to graph them using open or closed circles. 2) How to solve simple inequalities by using the same process as solving equations and boxing the variable. 3) How to graph the solutions of inequalities on a number line by placing open or closed circles above the solution number and drawing arrows in the appropriate direction based on making the inequality true.

2. Important Facts
< means ____ than
> means ______ than
≤ means ____________________________
≥ means ____________________________
Use an _____circle for < and > when graphing
Use a _______ circle for ≤ and ≥ when graphing

3. Important Facts
< means less than
> means greater than
Use an open circle for < and > when graphing.
Use a closed circle for ≤ and ≥ when graphing

4. How to solve an inequality
There is only one difference between an
equation and an inequality
= versus <, >, ≤, ≥

5. Solving inequalities
4 + x < 12
4 + x < 12 (draw T chart)
4 + x < 12(box in variable)
4 + x < 12 (minus 4 both sides)
-4 -4
x<8

6. Graphing
Why a closed circle for ≤ and ≥?
If something is on your graph there is a dot or line
on it. So, we use a regular dot or line to include
numbers in our answer.
Why an open circle for < and>?
If something is not on our graph we do not put a
dot or line on it. So, if 4 is not part of our answer
but 3.9999999999… is we can graph that by
putting an open circle to show we do not include
4 but we include numbers really really close to 4.

7. Now to graph the solution
x<8
1. Draw a number line. Just need a few numbers on
either side of the solution number.
2. Decide if open circle or closed circle. Place it above the
solution number.
3. Determine which way your arrow goes by substituting a
number in for the variable to make the statement true.
Then draw the arrow pointing in that direction.

8. Solving inequalities
48 ≥ 8 +m
48 ≥ 8+m (draw T chart, box variable)
-8 -8 (subtract 8 both sides)
40 ≥ m

9. Now to graph the solution
6≥m
1. Draw a number line. Just need a few numbers on
either side of the solution number.
2. Decide if open circle or closed circle. Place it above the
solution number.
3. Determine which way your arrow goes by substituting a
number in for the variable to make the statement true.
Then draw the arrow pointing in that direction.

10. 6u ≥ 36
u-6 ≥ 36
+6 + 6
u ≥ 42
39 40 41 42 43 44

11. y–1≥5
y–1≥5
+1 +1
y≥6
3 4 5 6 7 8

12. Graph an inequality
x < 12
1) Open circle or closed circle?
2) Which direction should the arrow go?
10 11 12 13 14

13. Graph an inequality
42 ≥ m
1) Open circle or closed circle?
2) Which direction should the arrow go?
40 41 42 43 44