Question

(1/5)^(х-1)+ (1/5)^(х+ 1) ≤26

Answer 1

$(frac{1}{5})^{x-1}+(frac{1}{5})^{x+1} leq 26\\(frac{1}{5})^{x-1}cdot Big (1+( frac{1}{5})^{x+1-(x-1)}Big ) leq 26 \\5^{1-x}cdot Big (1+(frac{1}{5})^2Big ) leq 26\\5^{1-x}cdot frac{26}{25} leq 26\\5^{1-x} leq 25\\5^{1-x} leq 5^2; ; Rightarrow ; ; ; 1-x leq 2\\1-2 leq x; ,; ; x geq -1\\xin [-1,+infty )$