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\(\frac{1}{\left|x-2\right|}>2\Rightarrow\left|x-2\right|< \frac{1}{2}\Rightarrow-\frac{1}{2}< x-2< \frac{1}{2}\)
\(\Rightarrow\frac{3}{2}< x< \frac{5}{2}\)
\(\Rightarrow A=\left(\frac{3}{2};\frac{5}{2}\right)\)
\(\left|x-1\right|< 1\Rightarrow-1< x-1< 1\Rightarrow0< x< 2\)
\(\Rightarrow B=\left(0;2\right)\)
\(\Rightarrow A\cup B=\left(0;\frac{5}{2}\right)\)
\(A\backslash B=[2;\frac{5}{2})\)
Nguyễn Huy TúAkai HarumaLightning FarronNguyễn Thanh HằngRibi Nkok NgokMysterious PersonVõ Đông Anh TuấnPhương AnTrần Việt Linh
\(\left|x-3\right|>4\Rightarrow\left[{}\begin{matrix}x-3>4\\x-3< -4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x>7\\x< -1\end{matrix}\right.\)
\(\Rightarrow A=\left(-\infty;-1\right)\cup\left(7;+\infty\right)\)
\(\left|2x-1\right|< 2\Leftrightarrow-2< 2x-1< 2\Leftrightarrow-\frac{1}{2}< x< \frac{3}{2}\)
\(\Rightarrow B=\left(-\frac{1}{2};\frac{3}{2}\right)\)
\(A\cap B=\varnothing\)
\(A\backslash B=A\)
\(A\cup B=\left(-\infty;-1\right)\cup\left(-\frac{1}{2};\frac{3}{2}\right)\cup\left(7;+\infty\right)\)
A=[-4;4]
B=[-3;2)
\(A\cap B\)=[-3;2)
A\B=[-4;-3)
B\A=\(\varnothing\)
Bài 3:
a: \(\left(-\infty;\dfrac{1}{3}\right)\cap\left(\dfrac{1}{4};+\infty\right)=\left(\dfrac{1}{4};\dfrac{1}{3}\right)\)
b: \(\left(-\dfrac{11}{2};7\right)\cup\left(-2;\dfrac{27}{2}\right)=\left(-\dfrac{11}{2};\dfrac{27}{2}\right)\)
c: \(\left(0;12\right)\text{\[}5;+\infty)=\left(0;5\right)\)
d: \(R\[ -1;1)=\left(-\infty;-1\right)\cup[1;+\infty)\)
\(x+2>m\)
\(x\le1\)
\(\Rightarrow x+2\le3\)
\(\Rightarrow m\le3\)