$$4(X-2)-5(X-6)=8(X+1)-3(2X+3)$$
$X = \frac{23}{3} = 7\frac{2}{3} \approx 7.666666667$
$$4X-8-5\left(X-6\right)=8\left(X+1\right)-3\left(2X+3\right)$$
$$4X-8-5X+30=8\left(X+1\right)-3\left(2X+3\right)$$
$$-X-8+30=8\left(X+1\right)-3\left(2X+3\right)$$
$$-X+22=8\left(X+1\right)-3\left(2X+3\right)$$
$$-X+22=8X+8-3\left(2X+3\right)$$
$$-X+22=8X+8-6X-9$$
$$-X+22=2X+8-9$$
$$-X+22=2X-1$$
$$-X+22-2X=-1$$
$$-3X+22=-1$$
$$-3X=-1-22$$
$$-3X=-23$$
$$X=\frac{-23}{-3}$$
$$X=\frac{23}{3}$$
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