TH1:
\(\left\{{}\begin{matrix}x-7\ge0\\x+3\ge0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x\ge7\\x\ge-3\end{matrix}\right.\\ \Leftrightarrow x\ge7\)
TH2:
\(\left\{{}\begin{matrix}x-7\le0\\x+3\le0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x\le7\\x\le-3\end{matrix}\right.\\ \Leftrightarrow x\le-3\)
Vậy `-3 <= x <=7`.
- Bài trước sai nhớ.
TH1:
\(\left\{{}\begin{matrix}x-7\ge0\\x+3\le0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x\ge7\\x\le-3\end{matrix}\right.\\ \Leftrightarrow VN.\)
TH2:
\(\left\{{}\begin{matrix}x-7\le0\\x+3\ge0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x\le7\\x\ge-3\end{matrix}\right.\\ \Leftrightarrow-3\le x\le7\)
Vậy `-3<=x<=7`.
Giải:
\(\left(x-7\right).\left(x+3\right)\le0\)
TH1:
\(\Rightarrow\left\{{}\begin{matrix}x-7\ge0\\x+3\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge7\\x\le-3\end{matrix}\right.\)
\(\Rightarrow\) (loại)
TH2:
\(\Rightarrow\left\{{}\begin{matrix}x-7\le0\\x+3\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\le7\\x\ge-3\end{matrix}\right.\)
\(\Rightarrow-3\le x\le7\)
Vậy \(x\in\left\{^+_-3;^+_-2;^+_-1;0;4;5;6;7\right\}\)
Chúc bạn học tốt!