$$\frac{1}{6}(x+5)=\frac{5}{12}(x+9)$$
$x = -\frac{35}{3} = -11\frac{2}{3} \approx -11.666666667$
$$\frac{1}{6}x+\frac{1}{6}\times 5=\frac{5}{12}\left(x+9\right)$$
$$\frac{1}{6}x+\frac{5}{6}=\frac{5}{12}\left(x+9\right)$$
$$\frac{1}{6}x+\frac{5}{6}=\frac{5}{12}x+\frac{5}{12}\times 9$$
$$\frac{1}{6}x+\frac{5}{6}=\frac{5}{12}x+\frac{5\times 9}{12}$$
$$\frac{1}{6}x+\frac{5}{6}=\frac{5}{12}x+\frac{45}{12}$$
$$\frac{1}{6}x+\frac{5}{6}=\frac{5}{12}x+\frac{15}{4}$$
$$\frac{1}{6}x+\frac{5}{6}-\frac{5}{12}x=\frac{15}{4}$$
$$-\frac{1}{4}x+\frac{5}{6}=\frac{15}{4}$$
$$-\frac{1}{4}x=\frac{15}{4}-\frac{5}{6}$$
$$-\frac{1}{4}x=\frac{45}{12}-\frac{10}{12}$$
$$-\frac{1}{4}x=\frac{45-10}{12}$$
$$-\frac{1}{4}x=\frac{35}{12}$$
$$x=\frac{35}{12}\left(-4\right)$$
$$x=\frac{35\left(-4\right)}{12}$$
$$x=\frac{-140}{12}$$
$$x=-\frac{35}{3}$$
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