$$\frac{x-8}{3}+\frac{2x+2}{12}+\frac{2x-1}{18}=3$$
$x = \frac{100}{11} = 9\frac{1}{11} \approx 9.090909091$
$$12\left(x-8\right)+3\left(2x+2\right)+2\left(2x-1\right)=108$$
$$12x-96+3\left(2x+2\right)+2\left(2x-1\right)=108$$
$$12x-96+6x+6+2\left(2x-1\right)=108$$
$$18x-96+6+2\left(2x-1\right)=108$$
$$18x-90+2\left(2x-1\right)=108$$
$$18x-90+4x-2=108$$
$$22x-90-2=108$$
$$22x-92=108$$
$$22x=108+92$$
$$22x=200$$
$$x=\frac{200}{22}$$
$$x=\frac{100}{11}$$
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