[tex]\left(\frac{1}{2}\right)^x\geq 2\sqrt{2} \\ \\ \left(\frac{1}{2}\right)^x\geq 2\sqrt{2} \\ \\ 2^{-x}\geq 2\cdot 2^{\frac{1}{2}} \\ \\ 2^{-x}\geq 2^{\frac{3}{2}} \\ \\ -x\geq \frac{3}{2} \ \ \ \ \ |\cdot (-1) \\ \\ x\leq -\frac{3}{2} \\ \\ x \in \left(-\infty,-\frac{3}{2} \right][/tex]
