HELP!!!

The only solution is x = -4.

Consider the equation as two separate equations: $5x + 3 = 4x - 1$ and $-(5x + 3) = 4x - 1$

Now, solve both equations for x as you normally would. Be careful of the negative in the second equation. 

Another way to do it (which is harder in this instance, is to square both sides

$|5x+3| = 4x - 1\\ 25x^2+30x+9=16x^2-8x+1\\ 9x^2+38x+8=0\\ x=\frac{-38\pm \sqrt{1156}}{18}\\ x=\frac{-38\pm 34}{18}\\ x=\frac{-19\pm 17}{9}\\ x=\frac{-2}{9}\qquad or \qquad x=\frac{-36}{9}\\ x=\frac{-2}{9}\qquad or \qquad x=-4\\ $

Check both answers in original equation and you will find that one of them is invalid.

So the other one is the answer.  :)