Download Solving Absolute Value Equations

Solving Absolute Value
Equations
Solving Absolute Value Equations
The Absolute Value Equality Principle
 x, if x  0 
Absolute value is define as x : 

  x, if x  0 
1)
If |A| = B, where B > 0, then A = B or A = -B

2)
If a number has a certain absolute value, then the
number is that value or it’s opposite value
If |A| = |B|, then A = B or A = -B

Two numbers have equal absolute values if they are
the same or if they are opposites of one another.
Solving Absolute Value Equations
Example 1: Solve 3|5 – 2x| – 2 = 19
If 3|5 – 2x| – 2 = 19
3|5 – 2x| = 21
|5 – 2x| = 7
 Divide both sides by 3
5 – 2x = 7
Thus,
5 – 2x = 7
- 2x = 2
x = -1
or
or
or
Therefore, s.s. = { -1, 6}
5 – 2x = -7
-2x = -12
x=6
Solving Absolute Value Equations
Example 2: Solve |x2 + 3x| = |6 + 2x|
If |x2 + 3x| = |6 + 2x|
then, x2 + 3x = 6 + 2x OR x2 + 3x = -(6 + 2x)
x2 + x – 6 = 0
OR x2 + 3x = – 6 – 2x
OR x2 + 5x + 6 = 0
thus, (x + 3)(x – 2) = 0 OR (x + 3)(x + 2) = 0
x + 3 = 0 or x – 2 = 0 OR x + 3 = 0 or x + 2 = 0
x = -3 or x = 2
OR
x = -3 or x = -2
Therefore, s.s. = {-3, 2, -2}
Homework

Do #11 – 19 all parts on page 177 from
Section 5.9 for Friday May 22nd 
Test #4 Tuesday May 26th!!!