Question

$2sqrt{2}*2 ^{x-3} geq frac{1}{2}$

Answer 1

$2sqrt{2}cdot 2 ^{x-3} geq dfrac{1}{2} \ \ 2cdot 2^{ frac{1}{2} }cdot 2 ^{x-3} geq 2^{-1} \ \ 2^{1+ frac{1}{2}+x-3 } geq 2^{-1}\ \ 1+ frac{1}{2}+x-3 geq -1\ \ x geq 0.5$