\(a.\)
\(-18-x=-8+\left(13\right)\)
\(\Rightarrow-18-x=5\)
\(\Rightarrow x=-18-5=-23\)
\(b.\)
\(x-43=\left(57-x\right)-50\)
\(\Rightarrow x-43=57-x-50\)
\(\Rightarrow x+x=43+57-50\)
\(\Rightarrow2x=50\)
\(\Rightarrow x=25\)
\(c.\)
\(-4\left(2x+9\right)-\left(-8x+3\right)-\left(x+13\right)=0\)
\(\Rightarrow-8x-36+8x-3-x-13=0\)
\(\Rightarrow-x-52=0\)
\(\Rightarrow-x=52\)
\(\Rightarrow x=-52\)