Tìm x biết

A.
|x|.(-2)+(-278)=508
\(\left|x\right|.\left(-2\right)=508-\left(-278\right)\)
\(\left|x\right|.\left(-2\right)=508+278\)
\(\left|x\right|.\left(-2\right)=786\)
\(\left|x\right|=786:\left(-2\right)\)
\(\left|x\right|=-393\)
Vì \(\left|x\right|\ge0\text{ mà }-393< x\Rightarrow\text{ không có giá trị x nào thỏa mãn}\)
Vậy không có giá trị x thỏa mãn.

B.|x|+x=0
*) \(x>0\Rightarrow\left|x\right|=x\)
\(\Rightarrow x+x=0\Rightarrow2x=0\Rightarrow x=0\Rightarrow\text{ loại }\)( không thỏa mãn x>0)
*) \(x< 0\Rightarrow\left|x\right|=-x\)
\(\Rightarrow\left|x\right|+x=0=-x+x=0\text{ (thỏa mãn)}\)
Vậy \(x\le0\text{ thì }\left|x\right|+x=0\)

C.
(-11). |x|=-22
\(\left|x\right|=-22:\left(-11\right)\)
\(\left|x\right|=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
\(\text{ Vậy }\left\{{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)

D.
x+(-2).3=45
\(x+\left(-6\right)=45\)
\(x=45-\left(-6\right)\)
\(x=45+6\)
\(x=51\)
Vậy \(x=51\)

E.
1+|2x-1|=2
\(\left|2x-1\right|=2-1\)
\(\left|2x-1\right|=1\)
\(\Rightarrow\left\{{}\begin{matrix}2x-1=1\\2x-1=-1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=2\\2x=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=1\\x=0\end{matrix}\right.\)
\(\text{Vậy }\left\{{}\begin{matrix}x=1\\x=0\end{matrix}\right.\)

F.
|x+15|-38=70
\(\left|x+15\right|=70+38\)
\(\left|x+15\right|=108\)
\(\Rightarrow\left\{{}\begin{matrix}x+15=108\\x+15=-108\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=93\\x=-123\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=93\\x=-123\end{matrix}\right.\)