Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 811

\[1)\ |6 - 2x| = 3x + 1\]

\[6 - 2x \geq 0\]

\[2x \leq 6\]

\[x \leq 3.\]

\[x \leq 3:\]

\[6 - 2x = 3x + 1\]

\[- 5x = - 5\]

\[x = 1.\]

\[x > 3:\]

\[- (6 - 2x) = 3x + 1\]

\[- 6 + 2x = 3x + 1\]

\[x = - 7.\]

\[Ответ:\ \ 1.\]

\[2)\ 2|x - 2| = |x| - 1\]

\[x - 2 \geq 0;\text{\ \ x} \geq 0\]

\[x \geq 2.\]

\[x \geq 2:\]

\[2(x - 2) = x - 1\]

\[2x - 4 = x - 1\]

\[x = 3.\]

\[0 \leq x < 2:\]

\[- 2(x - 2) = x - 1\]

\[- 2x + 4 = x - 1\]

\[- 3x = - 5\]

\[x = 1\frac{2}{3}.\]

\[x < 0:\]

\[- 2(x - 2) = - x - 1\]

\[- 2x + 4 = - x - 1\]

\[x = 5.\]

\[Ответ:\ \ 3;\ 1\frac{2}{3}.\]