Question

|x| +x = \(\frac{1}{3}\)

Answer 1

\(\left|x\right|+x=\frac{1}{3}\)

\(\Leftrightarrow\left|x\right|=\frac{1}{3}-x\)

+) Xét \(x\ge0\)

\(pt\Leftrightarrow x=\frac{1}{3}-x\)

\(\Leftrightarrow2x=\frac{1}{3}\)

\(\Leftrightarrow x=\frac{1}{6}\)( thỏa )

+) Xét \(x< 0\)

\(pt\Leftrightarrow x=x-\frac{1}{3}\)

\(\Leftrightarrow0x=\frac{-1}{3}\)( vô lí )

Vậy....

Answer 2

\(\left|x\right|+x=\frac{1}{3}\)

\(\Rightarrow\left|x\right|=\frac{1}{3}-x\)

\(\Rightarrow\left[{}\begin{matrix}x=\frac{1}{3}-x\\-x=\frac{1}{3}-x\end{matrix}\right.\)

\(\Rightarrow2x=\frac{1}{3}\)

\(\Rightarrow\)x=\(\frac{1}{6}\)

Vậy x=\(\frac{1}{6}\)