Задача 2А. Решите уравнение \(\left| {2x-1} \right| = 0,5\)
ОТВЕТ: 0,25; 0,75.Ответ
\(\left| {2x-1} \right| = 0,5.\) Уравнение вида \(\left| {f\left( x \right)} \right| = a\), где \(a \ge 0\), равносильно совокупности: \(\left[ {\begin{array}{*{20}{c}}{f\left( x \right) = a,\,\,\,}\\{f\left( x \right) = -a.}\end{array}} \right.\) \(\left| {2x-1} \right| = 0,5\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{2x-1 = 0,5,}\\{2x-1 = -0,5}\end{array}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \frac{3}{4},}\\{x = \frac{1}{4}.}\end{array}} \right.} \right.\) Ответ: \(\frac{1}{4};\;\;\frac{3}{4}.\)Решение