Question 114223: 6 - |4x - 3| = -19
how do i solve the following absolute value??
Answer by mathnard(10)   (Show Source):
You can put this solution on YOUR website! To solve an absolute value problem, you have to isolate the absolute value bars, and then make two equations. Here, I'll show you:
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 here, and -6 on this side also
multiply both sides by negative one:
 so now both sides are positive instead of negative.
now wouldn't you agree that if the problem was just
that "something" would have to be either 25 or -25?
well that's why
means
either  or 
if you solve the first one you get:
by solving the second one, we get:
So there are 2 solutions, or
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:
Do 4 times -5.5 to get
Now -22-3 equals -25 so:
and the absolute value of -25 is 25:
 which is true, so -5.5 works!!!
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