# Week 12-Solving Absolute value Equations

This we learn how to solve the solution of the absolute value Equation

First we learned how to use the graph to solve

Ex

this question is asking that what’s the x solution are by looking the graph

we can see the equation

|-3x+3|=9

The y intercept is 3

So there two possible inside the absolute

First:-3x+3=9

-3x=6

x=-2

Second:-(-3x+3)=9

3x-3=9

3x=12

x=4

And because of when the y=9 touch the linear the x=-2,4

so the solution are -2,4.

EX:Another example is about the x square

Formula:$4+2x=|x^2 +8x+12|$

First possible

x is positive

(x+2)(x+4)=0

x=-2,x=-4

Second posible

x is negative

(x+2)(x+8)=0

x=-2,x=-8

Because absolute can’t be the negative.so when x=-4 ,x=-8

4+2x is negative , so they can’t be the solution of this,

so the solution is x=-2