Solutions of an inequality

Question

With what value of a the solutions of the inequality are all real numbers?

1. 0.2^x+3 > a-2

2. (1/5)^x+3 > a^2-9a

Answer 1

1. 0.2^x+3 > a - 2. If a - 2 ≤ 0 or a ≤ 2 then 0.2^{x + 3} > a - 2 for all real x
2. (1/5)^{x + 3} > a² - 9a; a² - 9a ≤ 0; if 0 ≤ a ≤ 9 then (1/5)^{x + 3}_{> a}² - 9a for all real numbers x