\(A=2.\left|3x-1\right|-4=2.\left|3x-1\right|+\left(-4\right)\)
+Có: \(\left|3x-1\right|\ge với\forall x\)
\(\Rightarrow2.\left|3x-1\right|+\left(-4\right)\ge-4\)
\(\Leftrightarrow A\ge-4\)
+Dấu ''='' xảy ra khi \(\left|3x-1\right|=0\Leftrightarrow x=\frac{1}{3}\)
+Vậy Amin = -4 khi x = \(\frac{1}{3}\)
Đề chắc là rút gọn.
\(A=2.\left|3x-1\right|-4\)
\(A=6x-2-4\)
\(A=6x-6.\)
\(B=\left|x-2\right|+\left|x-4\right|\)
\(B=x-2+x-4\)
\(B=\left(x+x\right)+\left(-2-4\right)\)
\(B=2x-6.\)
\(C=\left|x-2\right|+\left|x-3\right|+\left|x-4\right|\)
\(C=x-2+x-3+x-4\)
\(C=\left(x+x+x\right)+\left(-2-3-4\right)\)
\(C=3x-9.\)
Chúc bạn học tốt!
\(B=\left|x-2\right|+\left|x-4\right|\\ \Leftrightarrow B=\left|x-2\right|+\left|4-x\right|\)
+Có: \(\left|x-2\right|\ge x-2với\forall x\\ \left|4-x\right|\ge4-xvới\forall x\)
\(\Rightarrow\left|x-2\right|+\left|4-x\right|\ge x-2+4-x\)
\(\Leftrightarrow B\ge2\)
+Dấu ''='' xảy ra khi
\(\left\{{}\begin{matrix}x-2\ge0\\4-x\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x\le4\end{matrix}\right.\)
\(\Rightarrow2\le x\le4\)
+Vậy Bmin= 2 khi 2 ≤ x ≤ 4
