Question

(1/5)^(х-1)+ (1/5)^(х+ 1) ≤26

Answer 1

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