Solve each of the following system of equation in `R :(2x+1)/(7x-1)>5,(x+7)/(x-8)>2`

Explanation

The given system of inequations is
`(2x+1)/(7x-1) gt 5`…(i)
and `(x+7)/(x-8) gt 2` …(ii)
Now, `(2x +1)/(7x-1)-5 gt 2`
` rArr ((2x+1)-5(7x-1))/(7x-1) gt 0`
` rArr (2x+1-35x+5)/(7x-1) gt 0`
` rArr (-33x+6)/(7x-1) gt 0 rArr (33x-6)/(7x-1) lt 0`
`rArr x in (1/7,6/33)` ....(iii)

and ` (x+7)/(x-8) gt 2 rArr (x+7)/(x-8) -2 gt 0`
`rArr (x+7-2(x-8))/(x-8) gt 0 rArr (x+7-2x+16)/(x-8) gt 0`
`rArr (-x+23)/(x-8) gt 0 rArr (x-23)/(x-8) lt 0`

`rArr x in (8, 23)`
Since, the intersection of Eqs. (iii) and (iv) is the null set. Hence, the given system equation has no solution.