$$\frac{ x-2 }{ 3 } = \frac{ x-3 }{ 4 } + \frac{ x-4 }{ 5 }$$
$x = \frac{53}{7} = 7\frac{4}{7} \approx 7.571428571$
$$20\left(x-2\right)=15\left(x-3\right)+12\left(x-4\right)$$
$$20x-40=15\left(x-3\right)+12\left(x-4\right)$$
$$20x-40=15x-45+12\left(x-4\right)$$
$$20x-40=15x-45+12x-48$$
$$20x-40=27x-45-48$$
$$20x-40=27x-93$$
$$20x-40-27x=-93$$
$$-7x-40=-93$$
$$-7x=-93+40$$
$$-7x=-53$$
$$x=\frac{-53}{-7}$$
$$x=\frac{53}{7}$$
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