[tex](2\sqrt[3]{2} )^{x+1}\geq( \sqrt{4\sqrt2}})^x\\\\(2\cdot2^{\frac{1}{3}} )^{x+1}\geq( \sqrt{2^2\cdot2^{\frac{1}{2}}}})^x\\\\(2^{1\frac{1}{3}} )^{x+1}\geq( \sqrt{2^{2\frac{1}{2}}}})^x\\\\(2^{\frac{4}{3}} )^{x+1}\geq( {2^{\frac{5}{2}})^{\frac{1}{2}})^x[/tex]
[tex]2^{\frac{4}{3}(x+1)}\geq 2^{\frac{5}{4}{x}}\\\\\frac{4}{3}(x+1)}\geq \frac{5}{4}{x}\ \ \ |\cdot12\\\\16(x+1)\geq 15x\\\\16x+16\geq 15x\\\\16x-15x\geq -16\\\\x\geq -16\\\\x\in<-16;+\infty)[/tex]
