Question

Answer 1

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

Trường hợp 1: \(x< -2\)

\(PT\Leftrightarrow-x-\dfrac{1}{2}+x+2=3\\ \Leftrightarrow\dfrac{3}{2}=3\left(vn\right)\)

Với \(-2\le x< -\dfrac{1}{2}\)

\(PT\Leftrightarrow-x-\dfrac{1}{2}-x-2=3\\ \Leftrightarrow-2x=\dfrac{11}{2}\Leftrightarrow x=-\dfrac{11}{4}\left(ktm\right)\Leftrightarrow x\in\varnothing\)

Với \(x\ge-\dfrac{1}{2}\)

\(PT\Leftrightarrow x+\dfrac{1}{2}-x-2=3\Leftrightarrow-\dfrac{3}{2}=3\left(vn\right)\)

Vậy PT vô nghiệm