1. 8.7 Solving Inequalities

2. Addition Property of Inequalities If a < b, then a + c < b + c
Subtraction Property of Inequalities If a < b, then a - c < b - c
The same is true for >,  , and 

3. Ex 1: Solve for “x” and graph: x - 3 > 4+3 +3
X > 7 -4 -8 8 4

4. Ex 2: Solve for “x” and graph: 8z + 6 – 7z  16-6 -6
z  10 -4 -8 8 4

5. Ex 3: Solve:

6. Multiplication and Division Property of Inequalities
When c is positive,
if a > b, then a • c > b • c
When c is negative,
if a > b, then a • c < b • c

7. Ex 4 Solve and graph
-3y  12 -3 -3
y  -4  -2 -6 -4 6 4 2

8. Ex 5: Solve and Graph.
3y  -15
y  -5 -2 -6 -4 6 4 2

9. Ex 6: Solve

10. Multi- Step Inequalities
Solve the same way as an equation:
1.) combine like terms
2.) Use Add/sub Prop of =
3.) Use Mult/ Div. Prop of =

11. Example7:
6 + 5y > 21
y >
5y > 15
y > 3

12. 3x + 4 ≤ 16 7x + 4  4x + 16 x  4 Example 8 : Solve and Graph -4x -4x-2 -6 -4 6 4 2

13. 17 –5y < 8y - 9 y > 2 -8y -8y 17 – 13y < -9 -17 -17
Example 9:
Solve
and
Graph
-8y
-8y
17 – 13y < -9
-17
-17
-13y < -26
Flip the inequality since we divided by a negative number!
-13
-13
y > 2 -2 -6 -4 6 4 2

14. Homework
Page 371 (12-52) even