b) \(-2x+\left(-3x\right)+\left(-4x\right)+......+\left(-20x\right)=1254\)
\(\Rightarrow x.\left(-2-3-4-.......-20\right)=1254\)
\(\Rightarrow x.\left[-\left(2+3+4+.....+20\right)\right]=1254\)
\(\Rightarrow x.\left(-209\right)=1254\)
\(\Rightarrow x=1254:\left(-209\right)\)
\(\Rightarrow x=-6\)
c) \(\left|2x\right|=4\)
\(\Rightarrow\orbr{\begin{cases}2x=4\\2x=-4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-2\end{cases}}\)
d) \(\left|2x-1\right|=3\)
\(\Rightarrow\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}\)