Question

giải BPT

a, lxl < 5

b, l2x+1l <3

c, lx-1l<2

Answer 1

\(a.\left|x\right|< 5\Leftrightarrow-5< x< 5\)

\(b.\left|2x+1\right|< 3\Leftrightarrow\left\{{}\begin{matrix}-3< 2x+1\\2x+1< 3\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x>-2\\x< 1\end{matrix}\right.\)\(\Leftrightarrow-2< x< 1\)

\(c.\left|x-1\right|< 2\Leftrightarrow\left\{{}\begin{matrix}x-1>-2\\x-1< 2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x>-1\\x< 3\end{matrix}\right.\)\(\Leftrightarrow-1< x< 3\)