a) \(-\left(12-5+9-x\right)=3-\left|5-8+2\right|\)
\(\Leftrightarrow-12+5-9-x=3-1\)
\(\Leftrightarrow-16-x=2\)
\(\Leftrightarrow x=-16-2\)
\(\Leftrightarrow x=-18\)
b) \(13-2\left|x-1\right|=-3\)
\(\Leftrightarrow2\left|x-1\right|=13+3\)
\(\Leftrightarrow2\left|x-1\right|=16\)
\(\Leftrightarrow\left|x-1\right|=8\)
\(\Rightarrow\left[{}\begin{matrix}x-1=8\Rightarrow x=9\\x-1=-8\Rightarrow x=-7\end{matrix}\right.\)
c) \(\left(2x-1\right)^3=27\)
\(\Leftrightarrow\left(2x-1\right)^3=3^3\)
\(\Rightarrow2x-1=3\)
\(\Leftrightarrow2x=4\)
\(\Leftrightarrow x=4:2=2\)
d) \(-5.\left(x-2\right)+4\left(x-3\right)=1\)
\(\Leftrightarrow-5x+10+4x-12=1\)
\(\Leftrightarrow-x-2=1\)
\(\Leftrightarrow-x=1+2=3\)
\(\Leftrightarrow x=-3\)
e) \(\left(x-1\right)\left(x+5\right)< 0\)
Do \(\left(x-1\right)\left(x+5\right)< 0\) nên \(x-1\) và \(x+5\) phải trái dấu.
Mà \(x-1< x+5\)
\(\Rightarrow\left\{{}\begin{matrix}x-1< 0\\x+5>0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x< 1\\x>-5\end{matrix}\right.\)
\(\Rightarrow-5< x< 1\)
Vậy \(x\in\left\{-4;-3;-2;-1;0\right\}\)