$$\frac{ 11(x-5) }{ 3 } + \frac{ 5(x-8) }{ 6 } = \frac{ 4(2-x) }{ 7 }$$
$x = \frac{366}{71} = 5\frac{11}{71} \approx 5.154929577$
$$14\times 11\left(x-5\right)+7\times 5\left(x-8\right)=6\times 4\left(2-x\right)$$
$$154\left(x-5\right)+7\times 5\left(x-8\right)=6\times 4\left(2-x\right)$$
$$154x-770+7\times 5\left(x-8\right)=6\times 4\left(2-x\right)$$
$$154x-770+35\left(x-8\right)=6\times 4\left(2-x\right)$$
$$154x-770+35x-280=6\times 4\left(2-x\right)$$
$$189x-770-280=6\times 4\left(2-x\right)$$
$$189x-1050=6\times 4\left(2-x\right)$$
$$189x-1050=24\left(2-x\right)$$
$$189x-1050=48-24x$$
$$189x-1050+24x=48$$
$$213x-1050=48$$
$$213x=48+1050$$
$$213x=1098$$
$$x=\frac{1098}{213}$$
$$x=\frac{366}{71}$$
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