$$\frac{x_{l}-5}{2}-\frac{x_{l}-3}{5}=\frac{1}{2}$$
$x_{l}=8$
$$5\left(x_{l}-5\right)-2\left(x_{l}-3\right)=5$$
$$5x_{l}-25-2\left(x_{l}-3\right)=5$$
$$5x_{l}-25-2x_{l}+6=5$$
$$3x_{l}-25+6=5$$
$$3x_{l}-19=5$$
$$3x_{l}=5+19$$
$$3x_{l}=24$$
$$x_{l}=\frac{24}{3}$$
$$x_{l}=8$$
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