$$\frac{4(x+2)}{3}-\frac{6(x-7)}{7}=12$$
$x=7$
$$7\times 4\left(x+2\right)-3\times 6\left(x-7\right)=252$$
$$28\left(x+2\right)-3\times 6\left(x-7\right)=252$$
$$28x+56-3\times 6\left(x-7\right)=252$$
$$28x+56-18\left(x-7\right)=252$$
$$28x+56-18x+126=252$$
$$10x+56+126=252$$
$$10x+182=252$$
$$10x=252-182$$
$$10x=70$$
$$x=\frac{70}{10}$$
$$x=7$$
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