1. 1.7 Solving Absolute Value Equations & Inequalities
p. 50

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. * Plug in answers to check your solutions!
Ex: Solve 6x-3 = 15
6x-3 = or 6x-3 = -15
6x = or 6x = -12
x = 3 or x = -2
* Plug in answers to check your solutions!

6. Get the abs. value part by itself first!
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
Check the solutions.

7. 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

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

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

10. Assignment