$$\frac { 1 } { 3 } ( 5 - 3 x ) \lt \frac { 2 } { 5 } ( 3 - 7 x )$$
$x<-\frac{7}{27}$
$$\frac{1}{3}\times 5+\frac{1}{3}\left(-3\right)x<\frac{2}{5}\left(3-7x\right)$$
$$\frac{5}{3}+\frac{1}{3}\left(-3\right)x<\frac{2}{5}\left(3-7x\right)$$
$$\frac{5}{3}+\frac{-3}{3}x<\frac{2}{5}\left(3-7x\right)$$
$$\frac{5}{3}-x<\frac{2}{5}\left(3-7x\right)$$
$$\frac{5}{3}-x<\frac{2}{5}\times 3+\frac{2}{5}\left(-7\right)x$$
$$\frac{5}{3}-x<\frac{2\times 3}{5}+\frac{2}{5}\left(-7\right)x$$
$$\frac{5}{3}-x<\frac{6}{5}+\frac{2}{5}\left(-7\right)x$$
$$\frac{5}{3}-x<\frac{6}{5}+\frac{2\left(-7\right)}{5}x$$
$$\frac{5}{3}-x<\frac{6}{5}+\frac{-14}{5}x$$
$$\frac{5}{3}-x<\frac{6}{5}-\frac{14}{5}x$$
$$\frac{5}{3}-x+\frac{14}{5}x<\frac{6}{5}$$
$$\frac{5}{3}+\frac{9}{5}x<\frac{6}{5}$$
$$\frac{9}{5}x<\frac{6}{5}-\frac{5}{3}$$
$$\frac{9}{5}x<\frac{18}{15}-\frac{25}{15}$$
$$\frac{9}{5}x<\frac{18-25}{15}$$
$$\frac{9}{5}x<-\frac{7}{15}$$
$$x<-\frac{7}{15}\times \frac{5}{9}$$
$$x<\frac{-7\times 5}{15\times 9}$$
$$x<\frac{-35}{135}$$
$$x<-\frac{7}{27}$$
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