How the heck do i solve this? My teacher gave me this without

>>8432054
absolute values are dumb, just remove it and solve it normally

>>8432084
I don't think it works like that, aren't you supposed to have more than one solution?

>>8432054
Solve it using |x| = x and |x| = -x

>>8432054
Four cases:

1) 2x-4>0 and 4x+1>0 (x>2 and x>-1/4, so x>2)
2x-4=3x-5+4x+1
2) 2x-4>0 and 4x+1<0 (x>2 and x<-1/4, so nothing)
2x-4=3x-5-4x-1
3) 2x-4<0 and 4x+1>0 (x<2 and x>-1/4, so -1/4<x<2)
-2x+4=3x-5+4x+1
4) 2x-4<0 and 4x+1<0 (x<2 and x<-1/4, so x<-1/4)
-2x+4=3x-5-4x-1

>>8432054
consider the cases where each of the eqns inside your abs brackets if greater >= or < 0. Drawing a number line could make it easier.

>>8432245
What do you mean by number line?

Square both sides as any real number squared cannot be negative

File: happyhelper.png (47KB, 778x512px) Image search: [Google]

47KB, 778x512px

>>8432211
To elaborate, keep the less-than/greater-than constraints in mind when you arrive at a solution for each of the three equations. I say "three equations" because #2's constraints are contradictory; x cannot be both greater than 2 and less than -1/4. Therefore, you can immediately eliminate #2 as a solution, giving three remaining equations to work with.

Solving #1 gives [math]x = 0[/math].

Keep in mind, however, that we have the additional constraint [math]x>2[/math].

0 is not greater than 2, so this is not a possible solution to the equation. Accordingly, plugging zero into the equation doesn't work. We get [math]4 = -4[/math].

Continue this process for #3 and #4 and you should find that there is only one solution to the equation which satisfies all the constraints.

>>8432570
example:

---------0------------> x

x ----------0+++++++

>>8432695
Thank you, this made me understand that stupid stuff