# How do you solve #abs(x+10)=4x-8#?

##### 1 Answer

#### Explanation:

Your absolute value equation looks like this

Right from the start, you know that the solutions to this equation must satisfy the condition

#4x-8>0 <=> x>2#

That happens because the absolute value of a number, regardlesss if that number is positive or negative, is always **positive**.

#color(blue)( |a| = {(a",", "if " a>=0), (-a",", "if "a<0):})#

So, with this in mind, determine the equation's two possible solutions

*If*#(x+10)>0# ,*you have*

#|x+10| = x+10#

and the equation becomes

*If*#(x+10)<0# ,*you have*

#|x+10| = -(x+10) = -x-10#

This will get you

This solution, *extraneous solution* because it does not satisfy the contion

Therefore,