How do you solve # abs(4x - 2) = 10 #?

1 Answer
Aug 8, 2015

Answer:

#x = 3# or #x=-2#.

Explanation:

You're dealing with an absolute value equation, which means that you need to take into account two possibilities for the modulus

  • if #4x-2>=0#, you have

#|4x-2| = 4x-2#

and the equation becomes

#4x-2 = 10#

#4x = 12 implies x = 12/4 = color(green)(3)#

  • If #4x-2<0#, then you have

#|4x-2| = -(4x-2) = -4x+2#

and the equation becomes

#-4x+2 = 10#

#-4x = 8 implies x = 8/(-4) = color(green)(-2)#

So, your equation has two possible solutions: #x=3# or #x=-2#.