Question

giúp mình với mn

giải bất pt:

a.\(\left\{{}\begin{matrix}2+x< 3+3x\\x-2\ge1-3x\end{matrix}\right.\)

b.\(\frac{1}{x-1}\le x-1\)

Answer 1

a/ \(\left\{{}\begin{matrix}2x>-1\\4x\ge3\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x>-\frac{1}{2}\\x\ge\frac{3}{4}\end{matrix}\right.\) \(\Rightarrow x\ge\frac{3}{4}\)

b/ \(x-1-\frac{1}{x-1}\ge0\)

\(\Leftrightarrow\frac{\left(x-1\right)^2-1}{x-1}\ge0\)

\(\Leftrightarrow\frac{x\left(x-2\right)}{x-1}\ge0\Rightarrow\left[{}\begin{matrix}x\ge2\\0\le x< 1\end{matrix}\right.\)