Absolute Value Equations

I.  Quiz

II.  Homework

III.   Equations Involving Absolute Values

Example:  

1)  Solve |x| = 2 Solution:  x = 2 or x = -2

2)  |x + 1| = 2

We have x + 1 = 2 or x + 1 = -2

x = 1 or x = -3.

3)  |3x - 4| = 5 We write

3x - 4 = 5 or 3x - 4 = -5

3x = 9 or 3x = -1

x = 3 or x = -1/3

Exercises

A)  |x| = 6

B)  |x - 3| = 6

C)  |x| = -4

D)  |2x + 1| = 7

III.  Equations That have Absolute Value Signs on Both Sides

If we have absolute value signs on both sides of the equation, we can play the same game with two choices as follows.

Example:  Solve |3x + 4| = | 2x - 3|

We can write

3x + 4 = 2x - 3 or 3x + 4 = -(2x - 3)

3x + 4 = 2x - 3 or 3x + 4 = -2x + 3  Now subtract 4 from both sides

3x = 2x - 7 or 3x = -2x - 1  Bring the x's to the left hand side

x = -7 or 5x = -1

x = -7 or x  = -1/5