1. Solving Absolute Value Equations & Inequalities
Standard
MM2A1c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

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. Your Turn: Solve 2x - 5 = 9

8. How do you solve absolute value inequalities?
First, isolate the absolute value expression on the left side of the inequality
Then choose the form of your inequality

9. Rewrite as
ax+b < c
And
ax+b > -c,
solve for x
Rewrite as
ax+b ≤ c
And
ax + b > -c,
solve for x
Rewrite as
ax + b > c Or
ax + b < -c,
solve for x
Rewrite as
ax + b ≥ c Or
ax + b ≤ -c,
solve for x

10. Solve
Solve

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

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

13. Your Turn: Solve & graph.

14. Homework: