1. Solve absolute value equations in 1 and 2 var. Solve absolute value inequalities in 1 and 2 var The learner will

2. Solving Inequalities Reminder Add this to the left “aha” column of your notes

3. We will use this rule in todays lesson trick < ….. Is less than….think….is less thAND >……is greater than….think…..is greatOR Solve Absolute Value Inequalities (1 var.) Add this to the left “aha” column of your notes

4. How to solve an absolute value equation (1 var.) If = 6….then x could be either ______ or _______ -66

5. How to solve an absolute value equation (1 var.) If = 6….then x could be either ______ or _______ +2 +2 -2 -2 X = {-3, 7} x – 2 = 5 or -x + 2 = 5 -66 x = 7 or -x = 3

6. Solve/Graph Absolute Value Equations

7. Solve Absolute Value Inequality (1 Var) |-2x +7| + 5 ≥ 14 x ≤ -1 OR x ≥ 8 - 5 |-2x +7| ≥ 9 -2x + 7 ≥ 9 or 2x - 7 ≥ 9 - 7 + 7 +7 -2x ≥ 2 or 2x ≥ 16 - 2 2 2 8

8. Solve/Graph Absolute Value Inequalities 6 21-9 2 1

9. Now...2 variables… We will not use shifting(translating) the parent function today – it will be shown soon!

10. 2 Equations: y = x + 2 - 4 y = x - 2 y = -x - 2 - 4 y = -x - 6 Enter the absolute value equation in the TI84 to see the graph Discuss: My 2 equations produce 2 lines, but the graph looks like a “V”….how could the 2 lines make that graph? Absolute Value Equation (2 Var.)

11. Equation: Vertex: (-2,-4) Equations: y=x-2 y=-x-6 -2 -x-6 x-2 Graph changes from a negative slope to a positive slope at x = – 2

12. y= Graph changes slope at x=1 Absolute Value Inequality (2 Var.)