Absolute Value Equations MATH 017 Intermediate Algebra S. Rook

2 Overview Section 2.6 in the textbook –Definition of Absolute Value –Solving Absolute Value Equations –Isolating the Absolute Value

Definition of Absolute Value

4 Absolute Value: Distance from 0 as viewed on a number line –Thus can only be positive or 0 If |x| = a, then x = a or x = -a

5 Definition of Absolute Value (Example) Ex 1: Solve: |x| = 3

6 Definition of Absolute Value (Example) Ex 2: Solve: |y| = 11

7 Definition of Absolute Value (Example) Ex 3: Solve: |z| = -1

Solving Absolute Value Equations

9 Solving Absolute Value Equations (Example) Ex 4: Solve: |2x + 3| = 9

10 Solving Absolute Value Equations (Example) Ex 5: Solve: |4x – 5| = 15

11 Solving Absolute Value Equations (Example) Ex 6: Solve:

Isolating the Absolute Value

13 Isolating the Absolute Value Before applying the definition of absolute value, the absolute value must be ISOLATED first –VERY important! –The absolute value must be ISOLATED before the definition of absolute value can be applied!

14 Isolating the Absolute Value (Example) Ex 7: Solve: |3x + 8| - 7 = 13

15 Isolating the Absolute Value (Example) Ex 8: Solve: 4|2x – 5| = 80

16 Isolating the Absolute Value (Example) Ex 9: Solve: 2|5x – 6| + 40 = 50

17 Isolating the Absolute Value (Example) Ex 10: Solve: |y – 3| + 7 = -2

18 Summary After studying these slides, you should know how to do the following: –Know the definition of absolute value and apply it to solve simple equations –Solve more complicated absolute value equations –Isolate the absolute value before solving an equation