Question

Giải BPT |2x-1| ≤x+2

Answer 1

Lời giải:BPT \(\Leftrightarrow \left\{\begin{matrix} x+2\geq 0\\ (2x-1)^2\leq (x+2)^2\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ 4x^2-4x+1\leq x^2+4x+4\end{matrix}\right.\)

\(\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ 3x^2-8x-3\leq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ (x-3)(3x+1)\leq 0\end{matrix}\right.\)

\(\Leftrightarrow \left\{\begin{matrix} x\geq -2\\ \frac{-1}{3}\leq x\leq 3\end{matrix}\right.\Rightarrow -\frac{1}{3}\leq x\leq 3\)