\(\left|x\right|-3+6=16\\ \left|x\right|=13\Rightarrow x=\pm13\)
\(35-\left|2x-1\right|=14\\ \left|2x-1\right|=21\\ \left(2x-1\right)^2=21^2\\ \left(2x-1+21\right)\left(2x-1-21\right)=0\\ 4\left(x+10\right)\left(x-11\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-10\\x=11\end{matrix}\right.\)
\(\left|3x-2\right|+5=9-x\\ \left|3x-2\right|=4-x\\ \Rightarrow\left(3x-2\right)^2=\left(4-x\right)^2\\ \left(3x-2-4+x\right)\left(3x-2+4-x\right)=0\\ 4\left(2x-3\right)\left(x+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}2x-3=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-1\end{matrix}\right.\)
\(x-\left(-25+7\right)>12-\left(15-14\right)\\ x+18>11\\ x>-7\)
\(\left|17+\left(x-15\right)\right|< 5\\ \left|x+2\right|< 5\\ \Rightarrow-5< x+2< 5\\ -7< x< 3\)
1) \(\left|x\right|-3+6=16\)
\(\left|x\right|-3=16-6\)
\(\left|x\right|-3=10\)
\(\left|x\right|=13\) \(\rightarrow\) \(x=\pm13\)
2) \(35-\left|2x-1\right|=14\)
\(\left|2x-1\right|=21\)
\(\left(2x-1\right)^2=21^2\)
\(\left(2x-1+21\right)\left(2x-1-21\right)=0\)
\(4\left(x+10\right)\left(x-11\right)=0\)
\(\Rightarrow\) \(\left[{}\begin{matrix}x=-10\\x=11\end{matrix}\right.\)
3) \(\left|3x-2\right|+5=9-x\)
\(\left|3x-2\right|=4-x\)
\(\Rightarrow\left(3x-2\right)^2=\left(4-x\right)^2\)
\(\left(3x-2-4+x\right)\left(3x-2+4-x\right)=0\)
\(4\left(2x-3\right)\left(x+1\right)=0\)
\(\Rightarrow\) \(\left[{}\begin{matrix}2x-3=0\\x+1=0\end{matrix}\right.\) \(\Rightarrow\) \(\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-1\end{matrix}\right.\)
4) \(x-\left(-25+7\right)>12-\left(15-14\right)\)
\(\Leftrightarrow x+18>11\)
\(x>-7\)
5) \(\left|17+\left(x-15\right)\right|< 5\)
\(\Leftrightarrow\) \(\left|x+2\right|< 5\)
\(-5< x+2< 5\)
\(\Rightarrow\) \(-7< x< 3\)
