$$\frac{x-6}{4}-\frac{x-4}{6}=1-\frac{x}{10}$$
$x=10$
$$15\left(x-6\right)-10\left(x-4\right)=60-6x$$
$$15x-90-10\left(x-4\right)=60-6x$$
$$15x-90-10x+40=60-6x$$
$$5x-90+40=60-6x$$
$$5x-50=60-6x$$
$$5x-50+6x=60$$
$$11x-50=60$$
$$11x=60+50$$
$$11x=110$$
$$x=\frac{110}{11}$$
$$x=10$$
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