a) $5+x=9-10⇔x=-1-5=-6^{}$
b) $x-3=7⇔x=7+3=10^{}$
c) $|x-2|=8⇔^{}$ \(\left[ \begin{array}{l}x-2=8\\x-2=-8\end{array} \right.\)⇔\(\left[ \begin{array}{l}x=10\\x=-6\end{array} \right.\)
d) $2×|x-1|=-7-21⇔|x-1|=-14 ⇒^{}$ Phương trình vô nghiệm vì $|x-1|≥0$
e) $2×x-18=10⇔2x=28⇔x=14^{}$
f) $2|x-3|+5=9⇔|x-3|=2⇔$\(\left[ \begin{array}{l}x-3=2\\x-3=-2\end{array} \right.\)⇔\(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\)