1. Solving Inequalities

2. The Solution of An Inequality is…
Any value of the variable that makes the inequality true
It is easier to understand the solution once it is graphed on a number line
MUST be written as a complete mathematical sentence (x > 5 rather than just 5)

3. When solving inequalities…
Use inverse operations
Treat the inequality symbol the same as an equal sign.

4. When the problem is backwards
-16 < x + 5
Move the –16 to the right and the x + 5 to the left
Flip over the inequality symbol
x + 5 > -16
Subtract 5 from both sides
x + 5 – 5 > -16 – 5
x > -21

5. What happens when you multiply both sides of an inequality by a negative?
-3 < 0
2 > -8
5 > 4
0 > -8

6. When multiplying or dividing both sides of an inequality by a negative
You must flip the inequality symbol!!!

7. Example -3x > 15 Divide both sides by –3 Flip the inequality symbol

8. Example 2
Flip the inequality
x > -128

9. Try these… x + 8 > -12 x – 12 < 17 x – 2 > -21

10. Try these…answers x + 8 > -12 x > -20 x – 12 < 17 x < 29

11. Try these…
5x > -15
-14 < 7x
-x > 3.4

12. Try these…answers 5x > -15 x > -3 -14 < 7x x > -2
5x > -15 x > -3
-14 < 7x x > -2
-x > x < -3.4
x < 2
x > -5/2 ½