Given-p-lt-x-lt-q-is-solution-set-inequality-1-2-x-2-2x-2-3x-gt-2-for-x-1-find-the-value-of-5p-3q-

Question Number 142968 by bramlexs22 last updated on 08/Jun/21

G i v e n p < x < q i s s o l u t i o n s e t

i n e q u a l i t y 1 + 2^{x} + 2^{2 x} + 2^{3 x} + \dots > 2

f o r x \neq 1 . f i n d t h e v a l u e o f

5 p - 3 q .

Answered by mr W last updated on 08/Jun/21

- 1 < 2^{x} < 1 \Rightarrow x < 0

\frac{1}{1 - 2^{x}} > 2 \Rightarrow 2^{x} > 2^{- 1} \Rightarrow x > - 1

\Rightarrow - 1 < x < 0

i . e . p = - 1, q = 0

5 p - 3 q = - 5

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