1. Brett Solberg – Alta High ‘11-’12
Inequalities
Brett Solberg – Alta High ‘11-’12

2. Warm-up
Get out your homework.
What problems do you want to review?

3. Today’s Agenda Inequalities Solving equations with many variables
Checking Solutions
Graphing
Solving
Solving equations with many variables

4. Review < less than > greater than ≤ less than or equal to
Inequalities use
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to
We use inequalities for problems with several solutions.

5. Curfew
You and your friends went to the Black vs. Blue game on Friday. You had permission to go as long as you came home before midnight.
When could you have
come home and make curfew?

6. Solutions to Inequalities
A solution is any number that makes the inequality true.
x = the time you come home
x < 12:00 AM

7. Checking Solutions
3 – x < 2; 4
2x + 1 ≥ 8; 2, 3, 4

8. Speeding
While mourning the near victory, you lost track of time and need to get home fast. If the speed limit is 65 mph on the freeway, graph how fast can you go without worrying about getting a speeding ticket?

9. Graphing Review < > use an open circle ≤ ≥ use a closed circle
Less than
Greater than
< > use an open circle
≤ ≥ use a closed circle
x ≥ -1 x < 3

10. Speeding
While mourning the near victory, you lost track of time and need to get home fast. If the speed limit is 65 mph on the freeway, graph how fast can you go without worrying about getting a speeding ticket?

11. Solving Inequalities Same as Equations with one exception.
Switch inequality signs if you multiply or divide both sides by a negative number.
-2x -1 > 2
-2x > 3
x < -3/2

12. Solving Multi-Variable Equations
Treat the other variables just like numbers
If there are 2 of the variable you are solving for you may need to factor.
A = (1/2)*b*h
2A = b*h
(2A)/b = h