Algebra – Inequalities and Exponents

Solve:

(a) 7^(4-16x) > 1
(b) 2/(x-1) < 1

(a) For any a^b > 1, if a > 1 then b should be greater than 0.

Hence 4 – 16x > 0

Therefore, x<1/4.

(b) 2/(x-1) < 1

2/(x-1) – 1< 0

[2-(x-1)]/(x-1) < 0

(3-x)/(x-1) < 0

(x-3)/(x-1) > 0

Hence ‘x’ lies outside the roots ‘1’ and ‘3’.

Therefore, x € (-∞ , 1) U (3, ∞)