Question

2x+1/4x-1 is greater than 5 and x+4/x-8 is greater than 2 ...Find the Range Of Common Inequalities , Class 11th​

Answer 1

Step-by-step explanation:

2x+1/4x-1 is greater than 5

let's take x greater than 1/4

so that inequality doesn't change sign

on shifting 4x-1 on other side

2x+1 is greater than 5(4x-1)

2x +1 is greater than 20x-5

this implies 18x is greater than 6

x is less than 1/3

if x is less than 1/4 then inequality will change sign

2x+1 is less than 20x - 5

x is greater than 1/3 which is not possible as x is less than 1/4

x will have to be between 1/4 &1/3

x+4 /x-8 is greater than 2

let x is greater than 8 so that inequality doesn't change sign on shifting x-8 on other side

x+4 is greater than 2x-16

x is less than 20

if x is less than 8 than inequality will change sign

x+4 is less than 2x-16

x is greater than 20

which is not possible

x will have to lie between 8 and 20 only

combined solution is

x belongs to (1/4,1/3)U(8,20).

I hope so I answered the question.

thanks