$$\frac{ 5x-3 }{ 3 } - \frac{ 3x+4 }{ 5 } = \frac{ 3 }{ 4 } -x$$
$x = \frac{153}{124} = 1\frac{29}{124} \approx 1.233870968$
$$20\left(5x-3\right)-12\left(3x+4\right)=45-60x$$
$$100x-60-12\left(3x+4\right)=45-60x$$
$$100x-60-36x-48=45-60x$$
$$64x-60-48=45-60x$$
$$64x-108=45-60x$$
$$64x-108+60x=45$$
$$124x-108=45$$
$$124x=45+108$$
$$124x=153$$
$$x=\frac{153}{124}$$
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