2.314 Найдите корень уравнения: a) 11,4b – (2,7b + 3,2b) + 2,35 = 6,2; б) 15d – (12,1d – 0,7d) + 5,6 = 20; в) $$3x + \frac{1}{6} - (3\frac{1}{2}x - 1\frac{1}{4}x) = 4\frac{2}{3}$$.

а) $$11,4b – (2,7b + 3,2b) + 2,35 = 6,2$$ $$11,4b - 5,9b + 2,35 = 6,2$$ $$5,5b = 6,2 - 2,35$$ $$5,5b = 3,85$$ $$b = \frac{3,85}{5,5} = \frac{385}{550} = \frac{7}{10} = 0,7$$ <p><strong>Ответ: b = 0,7</strong></p> б) $$15d – (12,1d – 0,7d) + 5,6 = 20$$ $$15d - 11,4d + 5,6 = 20$$ $$3,6d = 20 - 5,6$$ $$3,6d = 14,4$$ $$d = \frac{14,4}{3,6} = 4$$ <p><strong>Ответ: d = 4</strong></p> в) $$3x + \frac{1}{6} - (3\frac{1}{2}x - 1\frac{1}{4}x) = 4\frac{2}{3}$$ $$3x + \frac{1}{6} - (\frac{7}{2}x - \frac{5}{4}x) = \frac{14}{3}$$ $$3x + \frac{1}{6} - \frac{7}{2}x + \frac{5}{4}x = \frac{14}{3}$$ $$3x - \frac{7}{2}x + \frac{5}{4}x = \frac{14}{3} - \frac{1}{6}$$ $$\frac{12x}{4} - \frac{14x}{4} + \frac{5x}{4} = \frac{28}{6} - \frac{1}{6}$$ $$\frac{3x}{4} = \frac{27}{6}$$ $$3x = \frac{27}{6} \cdot 4$$ $$3x = \frac{27}{3} \cdot 2$$ $$3x = 9 \cdot 2$$ $$3x = 18$$ $$x = 6$$ <p><strong>Ответ: x = 6</strong></p>