Question

find all integral values of x which satisfy the the inequalities . 2(2-x)<4x-9<x+11.​

Answer 1

Answer:

$( \frac{13}{6} \: \: \: \: \: \: \: \: \frac{20}{3} )$

Step-by-step explanation:

$2(2 - x) < 4x - 9 < x + 11 \\ 4 - 2x < 4x - 9 < x + 11 \\ 4 - 2x + 9 < 4x < x + 11 + 9 \\ 13 - 2x < 4x < x + 20 \\ \\ 13 - 2x < 4x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4x < x + 20 \\ 13 < 6x \: \: \: \: \: \: \: \: \: \: \: \: 3x < 20 \\ x > \frac{13}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x < \frac{20}{3} \\ \\ x \: belongs \: to \: \: \: \: \: ( \frac{13}{6} \: \: \: \: \: \: \: \: \frac{20}{3} )$