We want to solve for x.
We take numbers to one side and variables to another:
[tex]\begin{gathered} -\frac{1}{6}-\frac{2}{5}x=-2-\frac{3}{4}x \\ -\frac{2}{5}x+\frac{3}{4}x=-2+\frac{1}{6} \\ \frac{-2(4)+3(5)}{5\cdot4}x=\frac{-2(6)+1}{6} \\ \frac{-8+15}{20}x=\frac{-12+1}{6} \\ \frac{7}{20}x=-\frac{11}{6} \end{gathered}[/tex]Now we isolate x by dividing both sides by (7/20). Remember dividing by a fraction means multiplying by its reciprocal. Thus,
[tex]\begin{gathered} x=\frac{-\frac{11}{6}}{\frac{7}{20}} \\ x=-\frac{11}{6}\times\frac{20}{7} \\ x=-\frac{110}{21} \end{gathered}[/tex]