Решебник по математике 6 класс Виленкин ФГОС Часть 1, 2 Часть 2. П. 5. Решение уравнений Задание 100

\[\boxed{\text{5.\ 100}}\]

\[\textbf{а)}\ 0,7x + 4 = 0,3x\]

\[0,7x - 0,3x = - 4\]

\[0,4x = - 4\]

\[x = - 4\ :0,4\]

\[x = - 10.\]

\[\textbf{б)} - 0,2x - 18 = 0,7x\]

\[- 0,2x - 0,7x = 18\]

\[- 0,9x = 18\]

\[x = 18\ :( - 0,9)\]

\[x = - 20.\]

\[\textbf{в)}\ 2x - 3\frac{1}{3} = \frac{5}{6}x + 2\frac{1}{2}\]

\[2x - \frac{10}{3} = \frac{5}{6}x + \frac{5}{2}\ \ \ \ | \cdot 6\]

\[12x - 20 = 5x + 15\]

\[12x - 5x = 15 + 20\]

\[7x = 35\]

\[x = 5.\]

\[\textbf{г)}\ 8,3 - 8n = - 6n - 31,7\]

\[- 8n + 6n = - 31,7 + 8,3\]

\[- 2n = - 23,4\]

\[n = 11,7.\]

\[\textbf{д)}\ \frac{3}{4}x - 1\frac{1}{4} = 1\frac{3}{8}x + 12,5\]

\[\frac{3}{4}x - \frac{5}{4} = \frac{11}{8}x + 12,5\ \ \ \ \ \ | \cdot 8\]

\[6x - 10 = 11x + 100\]

\[6x - 11x = 100 + 10\]

\[- 5x = 110\]

\[x = 110\ :( - 5)\]

\[x = - 22.\]

\[\textbf{е)}\ 5,5 - 7z = 5,8 - 10z\]

\[- 7z + 10z = 5,8 - 5,5\]

\[3z = 0,3\]

\[z = 0,3\ :3\]

\[z = 0,1.\]

\[\textbf{ж)}\ 4,6x = 7,2x\]

\[4,6x - 7,2x = 0\]

\[- 2,6x = 0\]

\[x = 0.\]

\[\textbf{з)} - 23x = 17x\]

\[- 23x - 17x = 0\]

\[- 40x = 0\]

\[x = 0.\ \]

\[\textbf{и)}\ 17x + 34 = 0\]

\[17x = - 34\]

\[x = - 34\ :17\]

\[x = - 2.\]