1. Graph Inequalities on a Number Line
SWBAT use a replacement set to identify the solution set of an inequality; graph the solution set of an inequality on a number line; write an inequality that describes a given graph

2. Definitions Replacement set Solution set Empty set
A set of numbers to be used as possible values for the variable in an equation or inequality
Solution set
Contains all the values for the variable that make the equation or inequality true
Empty set
A solution set that contains none of the numbers from the replacement set

3. Examples Inequality Replacement set Solution set y < 25
{24, 25, 26, …}
x > 8
{0, 1, 2, 3, …}
x ≤ 8
{4, 5, 6, 7, …}
t ≥ 10
{-3, -2, -1, 0, 1, 2, …}
t ≤ 10
{…, 8, 9, 10}
a < 0
{24}
{9, 10, 11, 12, …}
{4, 5, 6, 7, 8}
{10, 11, 12, 13, …}
{…8, 9, 10,} {}

4. Definitions Equivalent inequalities Graphing inequalities
Inequalities that have the same solution set
Graphing inequalities
the number is NOT included in solution set, use with < or >
the number IS included in the solution set, use with ≤ or ≥

5. Examples
x > 4
9 ≤ x
x ≤ 0
2> x

6. Try the problems on your sheet10 -5 5 15

7. Anwers
S={10, 12}
S={14, 15, 16, 17}
S={-1, 0, 1, 2, 3}
S={10, 20, 30, 40, …}
x ≥ -1
x < 4
x > -9