$$\frac{5x-2}{3}=\frac{4x+1}{2}$$
$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$
$$2\left(5x-2\right)=3\left(4x+1\right)$$
$$10x-4=3\left(4x+1\right)$$
$$10x-4=12x+3$$
$$10x-4-12x=3$$
$$-2x-4=3$$
$$-2x=3+4$$
$$-2x=7$$
$$x=\frac{7}{-2}$$
$$x=-\frac{7}{2}$$
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