Question

\(\left|x+\dfrac{1}{2}\right|-\sqrt{\dfrac{1}{4}}=\dfrac{3}{4}\)

Answer 1

\(\left|x+\dfrac{1}{2}\right|-\sqrt{\dfrac{1}{4}}=\dfrac{3}{4}\\ \Leftrightarrow\left|x+\dfrac{1}{2}\right|-\dfrac{1}{2}=\dfrac{3}{4}\\ \Leftrightarrow\left|x+\dfrac{1}{2}\right|=\dfrac{5}{4}\\ \Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{5}{4}\\x+\dfrac{1}{2}=\dfrac{-5}{4}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=-\dfrac{7}{4}\end{matrix}\right.\)