Given the equation:
[tex]\frac{2}{3}x-\frac{1}{2}=\frac{1}{3}+\frac{5}{6}x[/tex]
Adding 1/2 at both sides of the equal sign and combining similar terms:
[tex]\begin{gathered} \frac{2}{3}x-\frac{1}{2}+\frac{1}{2}=\frac{1}{3}+\frac{5}{6}x+\frac{1}{2} \\ \frac{2}{3}x+(-\frac{1}{2}+\frac{1}{2})=(\frac{1}{3}+\frac{1}{2})+\frac{5}{6}x \\ \frac{2}{3}x=(\frac{1\cdot2+1\cdot3}{6})+\frac{5}{6}x \\ \frac{2}{3}x=\frac{5}{6}+\frac{5}{6}x \end{gathered}[/tex]
Subtracting 5/6x at both sides of the equal sign and combining similar terms:
[tex]\begin{gathered} \frac{2}{3}x-\frac{5}{6}x=\frac{5}{6}+\frac{5}{6}x-\frac{5}{6}x \\ \frac{2\cdot2-5\cdot1}{6}x=\frac{5}{6}+(\frac{5}{6}x-\frac{5}{6}x) \\ -\frac{1}{6}x=\frac{5}{6} \end{gathered}[/tex]
Multiplying by -6 at both sides:
[tex]\begin{gathered} (-6)\cdot(-\frac{1}{6}x)=(-6)\cdot\frac{5}{6} \\ x=-5 \end{gathered}[/tex]
