$\displaystyle (x-4)/5 >= (2x+3)/2$
$\displaystyle 2(x-4) >= 5(2x+3)$
$\displaystyle 2x-8 >= 10x+15$
$\displaystyle -8-15 >= 8x$
$\displaystyle -23 >= 8x$
$\displaystyle (-23/8) >= x$
$\displaystyle x <= (-23/8)$
$\displaystyle (x-4)/5 >= (2x+3)/2$
$\displaystyle 2(x-4) >= 5(2x+3)$
$\displaystyle 2x-8 >= 10x+15$
$\displaystyle -8-15 >= 8x$
$\displaystyle -23 >= 8x$
$\displaystyle (-23/8) >= x$
$\displaystyle x <= (-23/8)$