a, $2x - 5 = -x - 17$
$\Leftrightarrow 2x + x = -17 + 5$
$\Leftrightarrow 3x = -12$
$\Leftrightarrow x = (-12) : 3$
$\Leftrightarrow x = -4$
b, $4 - \left | 2x - 1 \right | = -11$
$\Leftrightarrow \left | 2x - 1 \right | = 4 + 11$
$\Leftrightarrow \left | 2x - 1 \right | = 15$
$\Leftrightarrow \left[ \begin{array}{l}2x+1=15\\2x+1=-15\end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l}x=7\\x=-8\end{array} \right.$
c) $\left ( 2x - 3 \right )^{2} - 17 = 2^{3}$
$\Leftrightarrow \left ( 2x - 3 \right )^{2} - 17 = 8$
$\Leftrightarrow \left ( 2x - 3 \right )^{2} = 8 + 17$
$\Leftrightarrow \left ( 2x - 3 \right )^{2} = 25$
$\Leftrightarrow \left | 2x - 3 \right | = 5$
$\Leftrightarrow \left[ \begin{array}{l}2x-3=5\\2x-3=-5\end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l}x=4\\x=-1\end{array} \right.$
