Find x after simplifying the equation $\frac{3\mathrm{x}-4}{2}-\frac{(2\mathrm{x}-1)}{3}= \frac{1}{2}+\mathrm{x}$

Given equation is $\frac{3\mathrm{x}-4}{2}-\frac{(2\mathrm{x}-1)}{3}= \frac{1}{2}+\mathrm{x}$

Take the LCM of the equation on the left and right sides, we get:

$\frac{ 3(3\mathrm{x}-4)-2(2\mathrm{x}-1)}{6}=\frac{1+2\mathrm{x}}{2}$

$\frac{9\mathrm{x}-12-4\mathrm{x}+2}{6}=\frac{1+2\mathrm{x}}{2}$

$\frac{5\mathrm{x}-10}{6}=\frac{1+2\mathrm{x}}{2}$

$(5\mathrm{x}-10)=3(1+2\mathrm{x})$

x = - 13