Задача 15А. Решите уравнение \(\left| {2x + 4} \right| = \left| {x-1} \right|\)
ОТВЕТ: -5; -1.
\(\left| {2x + 4} \right| = \left| {x-1} \right|.\) Уравнение вида \(\left| {f\left( x \right)} \right| = \left| {g\left( x \right)} \right|\) равносильно совокупности: \(\left[ {\begin{array}{*{20}{c}}{f\left( x \right) = g\left( x \right),\,\,\,}\\{f\left( x \right) = -g\left( x \right).}\end{array}} \right.\) \(\left| {2x + 4} \right| = \left| {x-1} \right|\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{2x + 4 = x-1,\,\,}\\{2x + 4 = -x + 1}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = -5,}\\{x = -1.}\end{array}} \right.\) Ответ: \(-5;\;\;-1.\)