Уравнения с модулями. Задача 2

ОТВЕТ: 0,25;  0,75.

\(\left| {2x-1} \right| = 0,5.\)

Уравнение вида \(\left| {f\left( x \right)} \right| = a\), где \(a \ge 0\), равносильно совокупности:  \(\left[ {\begin{array}{*{20}{c}}{f\left( x \right) = a,\,\,\,}\\{f\left( x \right) = -a.}\end{array}} \right.\)

\(\left| {2x-1} \right| = 0,5\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{2x-1 = 0,5,}\\{2x-1 = -0,5}\end{array}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \dfrac{3}{4},}\\{x = \dfrac{1}{4}.}\end{array}} \right.} \right.\)

Ответ: \(\dfrac{1}{4};\;\;\dfrac{3}{4}.\)