1. 2.1/2.2 Solving Inequalities
Learning Goals:
create equations and inequalities in one variable and use them to solve problems

2. Interval Notation Symbols
Notation used to describe a range of values
Many times used in place of set-notation
Inequality Symbol
Graphing Symbol
Interval Notation Symbols
include a value
≤ or ≥ ●
[ , ]
reference a value
< or > ○
( , )

3. Notations and Their Graphs
Set-Notation
Interval Notation
Graph
{ y | y > -5 }
{ y | y ≤ 2 }
{ y | -2 ≤ y ≤ 7 }
{ y | y < 4 or y > 6}

4. Features of Inequalities
Inequalities have more than 1 solution
When you MULTIPLY or DIVIDE by a negative number you MUST flip the sign.
What happens if we multiply the inequality by –1 ?

5. EX 1 Solve & graph.

6. EX 2 Solve & graph.

7. For which values does this hold?
compound inequality: a pair of inequalities joined by AND or OR
Compound
“Key Word”
For which values does this hold?
What do I shade?
Example Graph
AND
where both are true
shade common parts only OR
where at least ONE is true
shade each part all on the same line

8. EX 3 Solve & graph.

9. EX 4 Solve & graph.

10. EX 5

11. ****Special Cases****
EX 6 Solve & graph.

12. ****Special Cases****
EX 7 Solve & graph.

13. EX 8 Solve & graph. EX 9 Solve & graph.