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

1 Answer
Aug 2, 2015

Answer:

#x = 6#

Explanation:

Your absolute value equation looks like this

#|x+10| = 4x-8#

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

#x+10 = 4x - 8 => x = 18/3 = color(green)(6)#

  • If #(x+10)<0#, you have

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

This will get you

#-x-10 = 4x+8 => x = color(red)(-18/5)#

This solution, #x=-18/5#, will be an extraneous solution because it does not satisfy the contion #x>2#.

Therefore, #x=6# is the only solution to this equation.