$$\frac{ x-1 }{ 3 } - \frac{ x+2 }{ 4 } + \frac{ x+3 }{ 5 } =1$$
$x = \frac{74}{17} = 4\frac{6}{17} \approx 4.352941176$
$$20\left(x-1\right)-15\left(x+2\right)+12\left(x+3\right)=60$$
$$20x-20-15\left(x+2\right)+12\left(x+3\right)=60$$
$$20x-20-15x-30+12\left(x+3\right)=60$$
$$5x-20-30+12\left(x+3\right)=60$$
$$5x-50+12\left(x+3\right)=60$$
$$5x-50+12x+36=60$$
$$17x-50+36=60$$
$$17x-14=60$$
$$17x=60+14$$
$$17x=74$$
$$x=\frac{74}{17}$$
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