Here:

$\displaystyle -7x + \frac {27}2x + \frac 92 = -2$ ...........subtract 9/2 from both sides

$\displaystyle \Rightarrow -7x + \frac {27}2x = - \frac {13}2$ ...........combine the x's on the left

$\displaystyle \Rightarrow \frac {13}2x = - \frac {13}2$ ............divide both sides by 13/2

$\displaystyle \Rightarrow \boxed{x = -1}$

now continue