Решебник по математике 6 класс Виленкин ФГОС Часть 1, 2 Часть 2. П. 6. Координаты на плоскости Задание 31

\[\boxed{\mathbf{6.31}}\]

\[\textbf{а)}\ \frac{1}{5}x = \frac{1}{2}x + 6\]

\[\frac{1}{5}x - \frac{1}{2}x = 6\]

\[\frac{2}{10}x - \frac{5}{10}x = 6\]

\[- \frac{3}{10}x = 6\]

\[x = 6\ :\left( - \frac{3}{10} \right) = - 6 \cdot \frac{10}{3}\]

\[x = - 20.\]

\[\textbf{б)}\ \frac{1}{4}x = \frac{1}{3}x + 1\ \]

\[\frac{1}{4}x - \frac{1}{3}x = 1\]

\[\frac{3}{12}x - \frac{4}{12}x = 1\]

\[- \frac{1}{12}x = 1\]

\[x = 1\ :\left( - \frac{1}{12} \right) = 1 \cdot ( - 12)\]

\[x = - 12.\]

\[\textbf{в)}\ \frac{8}{y} = \frac{2}{5}\]

\[y \cdot 2 = 8 \cdot 5\]

\[y = 40\ :2\]

\[y = 20.\]

\[\textbf{г)}\ \frac{3}{4} = \frac{x}{12}\]

\[4 \cdot x = 3 \cdot 12\]

\[x = 36\ :4\]

\[x = 9.\ \]