\(\left|x+1\right|+x=2\)
\(pt\Leftrightarrow\left|x+1\right|=2-x\)
\(\Leftrightarrow\left(\left|x+1\right|\right)^2=\left(2-x\right)^2\)
\(\Leftrightarrow x^2+2x+1=x^2-4x+4\)
\(\Leftrightarrow6x-3=0\Leftrightarrow6x=3\Leftrightarrow x=\dfrac{1}{2}\)