545. Решите уравнение: a) (2/3 x-4/5 )⋅15=8; б) (5/7 -2/3 y)⋅21=1; в) 2/3 x+7/3 x=18; г) 7/12 m+2/3 m-1/4 m=7.

545. Решите уравнение:

а) $$(\frac{2}{3}x - \frac{4}{5}) \cdot 15 = 8$$

$$ \frac{2}{3}x \cdot 15 - \frac{4}{5} \cdot 15 = 8 $$

$$ \frac{30}{3}x - \frac{60}{5} = 8 $$

$$ 10x - 12 = 8 $$

$$ 10x = 8 + 12 $$

$$ 10x = 20 $$

$$ x = \frac{20}{10} $$

$$ x = 2 $$

Ответ: $$ x = 2 $$

б) $$(\frac{5}{7} - \frac{2}{3}y) \cdot 21 = 1$$

$$ \frac{5}{7} \cdot 21 - \frac{2}{3}y \cdot 21 = 1 $$

$$ \frac{105}{7} - \frac{42}{3}y = 1 $$

$$ 15 - 14y = 1 $$

$$ -14y = 1 - 15 $$

$$ -14y = -14 $$

$$ y = \frac{-14}{-14} $$

$$ y = 1 $$

Ответ: $$ y = 1 $$

в) $$ \frac{2}{3}x + \frac{7}{3}x = 18 $$

$$ \frac{2+7}{3}x = 18 $$

$$ \frac{9}{3}x = 18 $$

$$ 3x = 18 $$

$$ x = \frac{18}{3} $$

$$ x = 6 $$

Ответ: $$ x = 6 $$

г) $$ \frac{7}{12}m + \frac{2}{3}m - \frac{1}{4}m = 7 $$

$$ \frac{7}{12}m + \frac{8}{12}m - \frac{3}{12}m = 7 $$

$$ \frac{7+8-3}{12}m = 7 $$

$$ \frac{12}{12}m = 7 $$

$$ 1m = 7 $$

$$ m = 7 $$

Ответ: $$ m = 7 $$