$$\frac { 1 } { 2 } x + \frac { 1 } { 5 } = \frac { 2 } { 3 } x - \frac { 1 } { 4 }$$
$x = \frac{27}{10} = 2\frac{7}{10} = 2.7$
$$\frac{1}{2}x+\frac{1}{5}-\frac{2}{3}x=-\frac{1}{4}$$
$$-\frac{1}{6}x+\frac{1}{5}=-\frac{1}{4}$$
$$-\frac{1}{6}x=-\frac{1}{4}-\frac{1}{5}$$
$$-\frac{1}{6}x=-\frac{5}{20}-\frac{4}{20}$$
$$-\frac{1}{6}x=\frac{-5-4}{20}$$
$$-\frac{1}{6}x=-\frac{9}{20}$$
$$x=-\frac{9}{20}\left(-6\right)$$
$$x=\frac{-9\left(-6\right)}{20}$$
$$x=\frac{54}{20}$$
$$x=\frac{27}{10}$$
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