Question 114223
To solve an absolute value problem, you have to isolate the absolute value bars, and then make two equations.  Here, I'll show you:

{{{6-abs(4x-3)=-19}}}


First, I'll subtract 6 from both sides.  Some people think you should add six to both sides because they see subtraction, but look at JUST the six.  Isn't it actually a positive six?  To "undo" a positive six, you subtract six (and I know it's positive because it always takes the sign just to the left...since there isn't a sign just to the left, we assume it's positive) 
{{{6-abs(4x-3)=-19}}}
-6 here, and -6 on this side also
{{{-abs(4x-3)=-25}}}


multiply both sides by negative one:
{{{abs(4x-3)=25}}} so now both sides are positive instead of negative.


now wouldn't you agree that if the problem was just 
{{{abs(something)=25}}}
that "something" would have to be either 25 or -25?
well that's why 
{{{abs(4x-3)=25}}} means
either {{{4x-3=25}}} or {{{4x-3=-25}}}


if you solve the first one you get:
{{{4x-3=25}}}
{{{4x=28}}}
{{{x=7}}}
by solving the second one, we get:
{{{4x-3=-25}}}
{{{4x=-22}}}
{{{x=-5.5}}}


So there are 2 solutions, {{{x=7}}} or {{{x=-5.5}}}

If you don't believe me, try plugging them back in!  It's a great way to check your answer!  See?  I'll plug -5.5 in:

{{{6-abs(4(-5.5)-3)=-19}}}  
Do 4 times -5.5 to get
{{{6-abs(-22-3)=-19}}}
Now -22-3 equals -25 so:
{{{6-abs(-25)=-19}}}
and the absolute value of -25 is 25:
{{{6-25=-19}}} which is true, so -5.5 works!!!