Question

|x+2| + |x-3| = 5

Answer 1

\(\left|x+2\right|+\left|x-3\right|=5\left(1\right)\)

Ta có :

\(\left|x+2\right|+\left|x-3\right|\ge\left|x+2+x-3\right|=\left|2x-1\right|\)

\(pt\left(1\right)\Leftrightarrow\left|2x-1\right|=5\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)