Given the initial expression
[tex]\begin{gathered} \frac{6x-5}{7}=\frac{2x-1}{3}+2 \\ \Leftrightarrow\frac{6x-5}{7}-\frac{2x-1}{3}-2=0 \end{gathered}[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow\frac{6x-5}{7}-\frac{(2x-1)}{3}=2 \\ \Rightarrow\frac{6x}{7}-\frac{5}{7}-\frac{2x}{3}+\frac{1}{3}=2 \\ \Rightarrow\frac{6x}{7}-\frac{2x}{3}=2+\frac{5}{7}-\frac{1}{3} \\ \Rightarrow\frac{4x}{21}=\frac{50}{21} \\ \Rightarrow x=\frac{50}{4}=\frac{25}{2} \\ \Rightarrow x=\frac{25}{2} \end{gathered}[/tex]Thus, the answer is x=25/2.
x=25/2 is the root of the equation
[tex]\frac{6x-5}{7}-\frac{2x-1}{3}-2=0[/tex]
