1. Solving Absolute Value Equations & Inequalities
You will ABSOLUTELY do this today in
Mr. Peter Richard’s
Very Awesome Class!

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

3. Ex: x = 5
What are the possible values of x?
x = or x = -5

4. 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.

5. Ex: Solve 6x-3 = 15
6x - 3 = 15 or 6x - 3 = x = 18 or 6x = x = 3 or x = -2 * Plug in answers to check your solutions!

6. Ex: Solve 2x = 8
Get the abs value alone by adding 3! 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 Check the solutions.

7. 6|5x + 2| = 312
Isolate the absolute value expression by dividing by 6.
6|5x + 2| = 312
|5x + 2| = 52
Set up two equations to solve.
5x + 2 = 52 5x + 2 = -52
5x = x = -54
x = 10 or x = -10.8
Check: 6|5x + 2| = |5x + 2| = 312
6|5(10)+2| = |5(-10.8)+ 2| = 312
6|52| = |-52| = 312
312 = = 312

8. 3|x + 2| -7 = 14 x + 2 = 7 x + 2 = -7 x = 5 or x = -9
Isolate the absolute value expression by adding 7 and dividing by 3.
3|x + 2| -7 = 14
3|x + 2| = 21
|x + 2| = 7
Set up two equations to solve.
x + 2 = x + 2 = -7
x = or x = -9
Check: 3|x + 2| - 7 = |x + 2| -7 = 14
3|5 + 2| - 7 = |-9+ 2| -7 = |7| - 7 = |-7| -7 = 14
= = 14
14 = = 14

9. Solving Absolute Value Inequalities
ax+b < c, where c>0
Becomes an “and” problem
Changes to: –c<ax+b<c
ax+b > c, where c>0
Becomes an “or” problem
Changes to: ax+b>c or ax+b<-c
In other words, change All Signs!

10. Ex: Solve & graph.
Becomes an “and” problem

11. Solve & graph. Get absolute value by itself first.
Becomes an “or” problem

12. Get To Work!
Quiz: Page 238 # 14, 16, 20, 26, 30
Homework: # 13, 17, 27, 37, 41