Задача 9А. Решите уравнение \(\left| x \right| = \left| {x + 2} \right|\)
ОТВЕТ: -1.
\(\left| x \right| = \left| {x + 2} \right|.\) Уравнение вида \(\left| {f\left( x \right)} \right| = \left| {g\left( x \right)} \right|\) равносильно совокупности: \(\left[ {\begin{array}{*{20}{c}}{f\left( x \right) = g\left( x \right),\,\,\,}\\{f\left( x \right) = -g\left( x \right).}\end{array}} \right.\) \(\left| x \right| = \left| {x + 2} \right|\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = x + 2\,\,\,}\\{x = -x-2}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{0 = 2,\,}\\{x = -1}\end{array}} \right.\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = -1.\) Ответ: \(-1.\)