Question

3^(2*x+1)+2*3^(2*x) <= 5^(2*x+1)-2*5^(2*x)

Answer 1

$3^{2x+1}+2* 3^{2x} leq 5^{2x+1}-2* 5^{2x}$
$3* 3^{2x}+2* 3^{2x} leq 5* 5^{2x}-2* 5^{2x}$
$5* 3^{2x} leq 3* 5^{2x}$
$3^{2x} leq frac{3}{5} * 5^{2x}$
$( frac{3}{5} )^{2x} leq frac{3}{5}$
$( frac{3}{5} )^{2x} leq ( frac{3}{5})^1$
$2x geq 1$
$x geq 0.5$
$x$ ∈ $[0.5;+$ ∞ $)$