$$\frac{x-2}{3}+\frac{x}{5}=\frac{2}{3}$$
$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$
$$5\left(x-2\right)+3x=10$$
$$5x-10+3x=10$$
$$8x-10=10$$
$$8x=10+10$$
$$8x=20$$
$$x=\frac{20}{8}$$
$$x=\frac{5}{2}$$
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