1. Using Multiplication & Division
Solving Inequalities
Using Multiplication & Division

2. Think about this inequality:
If it were an equation, you would know how to solve it.

3. Multiply both sides by 1/3.

4. Could you just do the same thing for an inequality?

5. Is the solution true? Solution:
Means that all numbers less than 9 should be true.
Substitute some of those numbers into the inequality to test : √ √ √

6. Will all numbers less than 9 make the sentence true?
As x gets smaller, 3x gets smaller and is definitely less than 27. But what about negative numbers? √ √ √
Negative numbers are always less than positive numbers!

7. So…we solve this inequality as we did with equations:√

8. Try this one: ?

9. Is the solution true? Solution:
Means that all numbers less than -9 should be true.
Substitute some of those numbers into the inequality to test :
NO!

10. New Rule!
If you multiply both sides of an equation by a negative number, you must FLIP the inequality symbol!

11. Solve again:
>

12. Is the solution true? Solution: Test numbers greater than 9:
What numbers are greater than -9? 5 10 15
-20
-15
-10 -5
-25 20 25 -9

13. √ √ √

14. Solve each inequality:

15. Answers: