$$\frac{ 3x-1 }{ 2 } - \frac{ 1-4x }{ 5 } = \frac{ 2x+3 }{ 7 }$$
$x=\frac{79}{141}\approx 0.560283688$
$$35\left(3x-1\right)-14\left(1-4x\right)=10\left(2x+3\right)$$
$$105x-35-14\left(1-4x\right)=10\left(2x+3\right)$$
$$105x-35-14+56x=10\left(2x+3\right)$$
$$105x-49+56x=10\left(2x+3\right)$$
$$161x-49=10\left(2x+3\right)$$
$$161x-49=20x+30$$
$$161x-49-20x=30$$
$$141x-49=30$$
$$141x=30+49$$
$$141x=79$$
$$x=\frac{79}{141}$$
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