We apply associative property to rearrange:
[tex]-4x+\frac{7}{2}+\frac{2}{3}=-9x+\frac{5}{6}[/tex]We solve the sum of similar terms:
[tex]-4x+\frac{7}{2}+\frac{2}{3}=-9x+\frac{5}{6}[/tex][tex]-4x+\frac{25}{6}=-9x+\frac{5}{6}[/tex]We add 9x to both sides (to cancel -9x):
[tex]-4x+9x+\frac{25}{6}=-9x+9x+\frac{5}{6}[/tex][tex]5x+\frac{25}{6}=\frac{5}{6}[/tex]We subtract 25/6 both sides (to cancel 25/6):
[tex]5x+\frac{25}{6}-\frac{25}{6}=\frac{5}{6}-\frac{25}{6}[/tex][tex]5x=\frac{-20}{6}[/tex]We divide by 5 both sides (to cancel 5):
[tex]\frac{5x}{5}=\frac{-20}{6\cdot5}[/tex][tex]x=\frac{-20}{30}[/tex]Finally we simplify the fraction:
[tex]x=\frac{-20}{30}=\frac{-4}{6}=\frac{-2}{3}[/tex]