solve |2x-1|=|3x+5|

 

$$\\|2x-1|=|3x+5|\\\\
2x-1=3x+5\qquad or \qquad 2x-1=-(3x+5)\\\\
2x=3x+6\qquad or \qquad 2x-1=-3x-5\\\\
-x=6\qquad or \qquad 2x=-3x-4\\\\
x=-6\qquad or \qquad 5x=-4\\\\
x=-6\qquad or \qquad x=\frac{-4}{5}\\\\
$check$\\\\
If\;\; x=-6\\\\
|-12-1|=|-18+5|\\\\
13=13\qquad True\\\\$$

 

$$\\If\;\; x=\frac{-4}{5}\\\\
|\frac{2*-4}{5}-1|=|\frac{3*-4}{5}+5|\\\\
|\frac{2*-4-5}{5}|=|\frac{3*-4+25}{5}|\\\\
|\frac{-13}{5}|=|\frac{13}{5}|\\\\
\frac{13}{5}= \frac{13}{5} \qquad True\\\\
$therefore the solutions are $\\\\
x=-6\;\;and \;\; x=\frac{-4}{5}\\\\$$

 

Here is the graphical solutions

 

https://www.desmos.com/calculator/rvzeay4sfu