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Solving Absolute Value Equations & Inequalities

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Solving Absolute Value Equations & Inequalities

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

-4 -3 -2 -1 0 1 2

- What are the possible values of x?
x = 5 or x = -5

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.

6x-3 = 15 or 6x-3 = -15

6x = 18 or 6x = -12

x = 3 or x = -2

* Plug in answers to check your solutions!

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.

- 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

- Becomes an “and” problem

-3 7 8

- Get absolute value by itself first.
- Becomes an “or” problem

-2 3 4