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