$$\frac{1}{5}(x-8)+\frac{4+x}{7}=7-\frac{23-x}{5}$$
$x=24$
$$7\left(x-8\right)+5\left(4+x\right)=245-7\left(23-x\right)$$
$$7x-56+5\left(4+x\right)=245-7\left(23-x\right)$$
$$7x-56+20+5x=245-7\left(23-x\right)$$
$$7x-36+5x=245-7\left(23-x\right)$$
$$12x-36=245-7\left(23-x\right)$$
$$12x-36=245-161+7x$$
$$12x-36=84+7x$$
$$12x-36-7x=84$$
$$5x-36=84$$
$$5x=84+36$$
$$5x=120$$
$$x=\frac{120}{5}$$
$$x=24$$
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