1. Solving Absolute Value Equations
Unit 3 Lesson 5.5
SWBAT write and solve absolute value equations.

2. What is Absolute Value?

3. Absolute Value (of x) Symbol lxl
The distance x is from 0 on the number line.
Always positive
Ex: l-3l=3

4. |-8| = 8
|4| = 4
You try:
|15| = ?
|-23| = ?

5. We can evaluate expressions that contain absolute value symbols.
Think of the | | bars as grouping symbols.
Evaluate |9x -3| + 5 if x = -2
|9(-2) -3| + 5
|-18 -3| + 5
|-21| + 5
21+ 5=26

6. To solve an absolute value equation:
ax+b = c, where c>0 To solve, set up 2 new equations, then solve each equation. ax+b = c or ax+b = -c ** make sure the absolute value is by itself before you split to solve.

7. Equations may also contain absolute value expressions
When solving an equation, isolate the absolute value expression first.
Rewrite the equation as two separate equations.
Consider the equation | x | = 3. The equation has two solutions since x can equal 3 or -3.
Solve each equation.
Always check your solutions.
Example: Solve |x + 8| = 3
x + 8 = 3 and x + 8 = -3
x = x = -11

8. Now Try These Solve |y + 4| - 3 = 0
|y + 4| = You must first isolate the variable by adding 3 to both sides.
Write the two separate equations.
y + 4 = 3 & y + 4 = -3
y = y = -7

9. Absolute value is never negative.
|3d - 9| + 6 = 0 First isolate the variable by
subtracting 6 from both sides.
|3d - 9| = -6
There is no need to go any further with this problem!
Absolute value is never negative.
Therefore, the solution is No Solution!

10. Solve: 3|x - 5| = 12
|x - 5| = 4
x - 5 = 4 and x - 5 = x = x = 1

11. 6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2
Ex: Solve 6x-3 = 15
6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2

12. Ex: Solve 2x = 8
Get the abs. value part by itself first! 2x+7 = 11 Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9

13. Solve: |8 + 5a| = 14 - a
8 + 5a = 14 - a and a = -(14 – a)
Set up your 2 equations, but make sure to negate the entire right side of the second equation.
8 + 5a = 14 - a and a = a
6a = a = a = a = -5.5
19.5 = 19.5

14. Absolute Deviation
Absolute deviation of a number x from a given value is the absolute value of the difference of x and the given value:
Absolute deviation = |x-given value|
The absolute deviation of x from 7.6 is 5.2.
|x – 7.6| = 5.2