Решебник по математике 6 класс Виленкин Часть 1, 2 Часть 2. Задачи на повторение 21

\[\boxed{\mathbf{П.\ 21}}\]

\[\textbf{а)}\ \frac{x - 0,7}{x + 0,3} = \frac{5,7}{4,7}\]

\[4,7 \cdot (x - 0,7) = 5,7 \cdot (x + 0,3)\]

\[4,7x - 3,29 = 5,7x + 1,71\]

\[4,7x - 5,7x = 1,71 + 3,29\]

\[- x = 5\]

\[x = - 5.\]

\[\textbf{б)}\ \frac{19,5}{n - 2,4} = \frac{47,25}{n + 1,3}\]

\[19,5 \cdot (n + 1,3) =\]

\[= 47,25 \cdot (n - 2,4)\]

\[19,5n + 25,35 = 47,25n - 113,4\]

\[19,5n - 47,25n =\]

\[= - 113,4 - 25,35\]

\[- 27,75n = - 138,75\]

\[n = 138,75\ :27,75 =\]

\[= 13\ 875\ :2775\]

\[n = 5.\]

\[\textbf{в)}\ \frac{m + 0,15}{4,1} = \frac{m - 2,4}{2,4}\]

\[2,4 \cdot (m + 0,15) =\]

\[= 4,1 \cdot (m - 2,4)\]

\[2,4m + 0,36 = 4,1m - 9,84\]

\[2,4m - 4,1m = - 9,84 - 0,36\]

\[- 1,7m = - 10,2\]

\[m = 10,2\ :1,7 = 102\ :17\]

\[m = 6.\]

\[\textbf{г)}\ \frac{2x - 4,16}{2,4} = \frac{5x - 6,16}{0,7}\]

\[0,7 \cdot (2x - 4,16) =\]

\[= 2,4 \cdot (5x - 6,16)\]

\[1,4x - 2,912 = 12x - 14,784\]

\[1,4x - 12x = - 14,784 + 2,912\]

\[- 1,6x = - 11,872\]

\[x = 11,872\ :1,6 = 118,72\ :16\]

\[x = 7,42.\]