$$\frac{x-7}{3}+\frac{2x+1}{2}=\frac{5}{6}$$
$x=2$
$$2\left(x-7\right)+3\left(2x+1\right)=5$$
$$2x-14+3\left(2x+1\right)=5$$
$$2x-14+6x+3=5$$
$$8x-14+3=5$$
$$8x-11=5$$
$$8x=5+11$$
$$8x=16$$
$$x=\frac{16}{8}$$
$$x=2$$
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