1. Lesson 2-7: Absolute Value Objective:  Students will simplify absolute value expressions  Students will solve and graph inequalities involving absolute value.

2. Definition of Absolute Value │x│ = x if x is positive │x│ = -x if x is negative Also, “distance from zero” → never negative Simplify with Absolute Value │a b│= │a │● │b │ → │7x │ = 7 │x │ │a n │ = a n, only if n is an even integer → │x -8 │ = x -8 Distance Distance between points a and b is │a - b │ or │b - a │

3. Absolute Value Equations For any expression E and positive number n: The solution to │E │ = n must satisfy E = n or E = -n Example 1 Solve │x + 3 │ = 5 Solving Absolutes 1)Isolate the Absolute value 2)Split up 3)Solve each 4)Graph (if required) x + 3 = 5 or x + 3 = -5 x = 2 or x = -8

4. Absolute Value Inequalities For any expression E and positive number n: The solution to │E │ -n The solution to │E │ > n must satisfy: E > n or E < -n Memory Tricks Sign Conjunction On Number Line Remember Less than And Between LAB Greater than Or Opposite GOO Splitting up → 1 st inequality: same 2 nd inequality: opposite symbol and sign

5. Example 2 Solve and graph 2│x - 3 │- 8 < 12 x - 3 -10 │x - 3 │< 10 x -7 -7 < x < 13 LAB

6. Example 3 Example 4 Simplify │-3y │ Simplify Example 5 Find the distance between 7 and -5 For odd powers: Take out the highest even power possible The highest power ever left inside is one

7. You Try Example 6: Solve and graph │2x - 4 │- 6 = 2

8. Example 7: Is this LA or GO? Solve and graph │2x - 5 │> 1