Задача 3. Решите уравнение \(\left| {4x} \right| = 3\)
ОТВЕТ: \( \pm \dfrac{3}{4}.\)Ответ
\(\left| {4x} \right| = 3.\) Уравнение вида \(\left| {f\left( x \right)} \right| = a\), где \(a \ge 0\), равносильно совокупности: \(\left[ {\begin{array}{*{20}{c}}{f\left( x \right) = a,\,\,\,}\\{f\left( x \right) = -a.}\end{array}} \right.\) \(\left| {4x} \right| = 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{4x = 3,\,\,}\\{4x = -3}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \dfrac{3}{4},\,\,\,}\\{x = -\dfrac{3}{4}.}\end{array}} \right.\) Ответ: \( \pm \dfrac{3}{4}.\)Решение