$$\frac{ 1-2x }{ 4 } - \frac{ 3-5x }{ 8 } = \frac{ 3-x }{ 2 } - \frac{ x-4 }{ 6 }$$
$x = \frac{55}{19} = 2\frac{17}{19} \approx 2.894736842$
$$6\left(1-2x\right)-3\left(3-5x\right)=12\left(3-x\right)-4\left(x-4\right)$$
$$6-12x-3\left(3-5x\right)=12\left(3-x\right)-4\left(x-4\right)$$
$$6-12x-9+15x=12\left(3-x\right)-4\left(x-4\right)$$
$$-3-12x+15x=12\left(3-x\right)-4\left(x-4\right)$$
$$-3+3x=12\left(3-x\right)-4\left(x-4\right)$$
$$-3+3x=36-12x-4\left(x-4\right)$$
$$-3+3x=36-12x-4x+16$$
$$-3+3x=36-16x+16$$
$$-3+3x=52-16x$$
$$-3+3x+16x=52$$
$$-3+19x=52$$
$$19x=52+3$$
$$19x=55$$
$$x=\frac{55}{19}$$
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