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a/ \(\left|2x-1,6\right|-2,3=1,4\)
\(\Leftrightarrow\left|2x-1,6\right|=3,7\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1,6=3,7\\2x-1,6=-3,7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=5,3\\2x=-2,1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2,65\\x=-1,05\end{matrix}\right.\)
Vậy ....
b/ \(5,4-\left|3x-1,2\right|=5,5\)
\(\Leftrightarrow\left|3x-1,2\right|=-0,1\)
Mà \(\left|3x-1,2\right|\ge0\)
\(\Leftrightarrow x\in\varnothing\)
c/ \(\left|x+1,3\right|+\left|x+2,4\right|=4x\)
Mà \(\left\{{}\begin{matrix}\left|x+1,3\right|\ge0\\\left|x+2,4\right|\ge0\end{matrix}\right.\) \(\Leftrightarrow4x\ge0\)
\(\Leftrightarrow x+1,3+x+2,4=4x\)
\(\Leftrightarrow2x+3,7=4x\)
\(\Leftrightarrow3,7=4x-2x\)
\(\Leftrightarrow2x=3,7\)
\(\Leftrightarrow x=1,85\)
Vậy ....
d/ \(\left|x-1,2\right|+\left|2,5-x\right|=0\)
Mà \(\left\{{}\begin{matrix}\left|x-1,2\right|\ge0\\\left|2,5-x\right|\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-1,2\right|=0\\\left|2,5-x\right|=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1,2=0\\2,5-x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1,2\\x=2,5\end{matrix}\right.\) (loại)
Vậy ..
a, \(\left|2x-1,6\right|-2,3=1,4\)
\(\Rightarrow\left|2x-1,6\right|=3,7\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1,6=3,7\\2x-1,6=-3,7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2,65\\x=-1,05\end{matrix}\right.\)
b,\(5,4-\left|3x-1,2\right|=5,5\)
\(\Rightarrow\left|3x-1,2\right|=-0,1\) (vô lí)
Vì \(\left|x\right|\ge0\) mà \(\left|3x-1,2\right|< 0\)
Vậy, không có giá trị của x thỏa mãn.
c, \(\left|x+1,3\right|+\left|x+2,4\right|=4x\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x+1,3\right|\ge0\\\left|x+2,4\right|\ge0\end{matrix}\right.\Leftrightarrow4x\ge0\)
\(\Leftrightarrow x+1,3+x+2,4=4x\)
\(\Leftrightarrow x+x+1,3+2,4=4x\)
\(\Leftrightarrow2x+3,7=4x\)
\(\Leftrightarrow2x-4x=-3,7\)
\(\Leftrightarrow-2x=-3,7\)
\(\Leftrightarrow x=\dfrac{3,7}{2}\)
d, \(\left|x-1,2\right|+\left|2,5-x\right|=0\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x-1,2\right|\ge0\\\left|2,5-x\right|\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-1,2\right|=0\\\left|2,5-x\right|=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1,2=0\\2,5-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1,2\\x=2,5\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3,2.x+\left(-1,2\right).x+2,7=-4,9\)
\(x.\left(3,2+\left(-1,2\right)\right)+2,7=-4,9\)
\(x.2+2,7=-4,9\)
\(x.2=-4,9-2,7=-7,6\)
\(x=-7,6:2=-3,8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\left|x\left(x-7\right)\right|=x\)
\(\Rightarrow\orbr{\begin{cases}x\left(x-7\right)=x\\x\left(x-7\right)=-x\end{cases}\Leftrightarrow\orbr{\begin{cases}x-7=1\\x-7=-1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=8\\x=6\end{cases}}}\)
b) \(\left|x-1,1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|=5x\)
\(\Rightarrow x-1,1+x+1,2+x+1,3+x+1,4=5x\)
\(\Leftrightarrow4x+2,8=5x\)
\(\Leftrightarrow x=2,8\)
\(a.\)\(\left|x.\left(x-7\right)\right|=x\)( Đk: \(x\ge0\))
\(\Leftrightarrow\orbr{\begin{cases}x.\left(x-7\right)=x\\x.\left(x-7\right)=-x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-7=x:x\\x-7=-x:x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-7=1\\x-7=-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1+7\\x=-1+7\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=8\\x=6\end{cases}}\)
\(b.\)\(\left|x-1,1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|=5x\)( Đk: \(5x\ge0\Leftrightarrow x\ge0\))
\(\Rightarrow x-1,1+x+1,2+x+1,3+x+1,4=5x\)
\(\Leftrightarrow\left(x+x+x+x\right)+\left(-1,1+1,2+1,3+1,4\right)=5x\)
\(\Leftrightarrow4x+2,8=5x\)
\(\Leftrightarrow2,8=5x-4x\)
\(\Leftrightarrow x=2,8\)
\(c.\)\(7^{x+2}+2.7^{x-1}=345\)
\(\Leftrightarrow7^{x-1}.7^{x+3}+2.7^{x-1}=345\)
\(\Leftrightarrow7^{x-1}.\left(7^{x+3}+2\right)=345\)
\(......................\)
Đến đây mk ko bt làm nữa, tự lm nhé !
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3,2x+\left(-1,2\right)x+2,7=-4,9\)
\(\Leftrightarrow2x+2,7=-4,9\)
\(\Leftrightarrow2x=-7,6\)
\(\Leftrightarrow x=-3,8\)
3,2x + ( -1,2 )x + 2,7 = -49
(3,2 + -1,2 )x = -49 - 2,7
2x = -51,7
x = -51,7 : 2
x = -25,85
\(\left|x-1,3\right|=2,7\)
\(\Leftrightarrow\orbr{\begin{cases}x-1,3=2,7\\x-1,3=-2,7\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=2,7+1,3\\x=-2,7+1,3\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=4\\x=-1,4\end{cases}}\)
\(\left|x+1,2\right|-2,6=4,5\)
\(\Leftrightarrow\left|x+1,2\right|=4,5+2,6\)
\(\Leftrightarrow\left|x+1,2\right|=7,1\)
\(\Leftrightarrow\orbr{\begin{cases}x+1,2=7,1\\x+1,2=-7,1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=7,1-1,2\\x=-7,1-1,2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=5,9\\x=-8,3\end{cases}}\)
P/s: Bn muốn để phân số hay số thập phân đều đc. @_@
\(\left|x-1,3\right|=2,7\)
\(\Rightarrow\orbr{\begin{cases}x-1,3=2,7\\x-1,3=-2,7\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2,7+1,3\\x=-2,7+1,3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=4\\-1,4\end{cases}}\)
Vậy \(x=4\) hoặc \(x=-1,4\)
b) \(\left|x+1,2\right|-2,6=4,5\)
\(\left|x+1,2\right|=4,5+2,6\)
\(\left|x+1,2\right|=7,1\)
\(\Rightarrow\orbr{\begin{cases}x+1,2=7,1\\x+1,2=-7,1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=7,1-1,2\\x=-7,1-1,2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=5,9\\x=-8,3\end{cases}}\)
Vậy \(x=5,9\)hoặc \(x=-8,3\)
Chúc bạn học tốt !!!