$-5| 2+4x | = -32(x+3/4)- | x | + 1$ This was my attempt:
$$-5| 2+4x | = -32\left(x+\frac34\right)- | x | + 1\\
\implies|2+4x|=\frac{-32x-24- | x | + 1}{-5}\\
\implies2+4x=\pm \frac{-32x+-24- x  + 1}{-5}\\
\implies4x=\pm \frac{-33x+-23 }{-5}-2\\
\implies-20x=\pm (-33x-23)+10\\
\implies-20x= -33x-13\text{ or} -20x=33x+33\\
\implies13x= -13\text{ or} -53x=33\\
\implies x=-1\text{ or} x=-\frac{33}{53}$$
Neither of these answers works when checking.
Using a graphing calculator I get an answer of $\frac{-11}{17}$ which does check, but I don't know how to get that answer using algebraic means.

Hint:
There are two equations here. When you have absolute value, you have to have one equation where you use the original and another where the stuff inside the absolute value signs is negative. So try solving the equation where the stuff in the absolute value signs are negative.
