Question

Solve the inequality 2x+1/7x-1 >5, x+7/x-8 >2

Answer 1

Answer:

No solution.

Step-by-step explanation:

Given :

$\displaystyle{\dfrac{2x+1}{7x-1} >5}$

Adding - 5 both side

$\displaystyle{\dfrac{2x+1}{7x-1} -5>5-5}$

$\displaystyle{\dfrac{2x+1}{7x-1} -5>0}$

$\displaystyle{\dfrac{2x+1-5(7x-1)}{7x-1} >0}$

$\displaystyle{\dfrac{2x+1-35x+5}{7x-1} >0}$

$\displaystyle{\dfrac{-33x+6}{7x-1} >0}$

$\displaystyle{\dfrac{-3(11x-2)}{7x-1} >0}$

Divide by - 3 both side

$\displaystyle{\dfrac{(11x-2)}{7x-1} <0}$

11 x - 2 < 0

x < 2 / 11

7 x - 1 < 0

x < 1 / 7

So . x €

$\displaystyle{\left(\frac{2}{11} \ , \frac{1}{7} \right)}$

Case 2 ) .

$\displaystyle{\dfrac{x+7}{x-8} >2}$

Adding - 2 both side :

$\displaystyle{\dfrac{x+7}{x-8}-2 >2-2}$

$\displaystyle{\dfrac{x+7}{x-8}-2 >0}$

$\displaystyle{\dfrac{x+7-2(x-8)}{x-8} >0}$

$\displaystyle{\dfrac{x+7-2x+16}{x-8} >0}$

$\displaystyle{\dfrac{-x+23}{x-8} >0}$

$\displaystyle{\dfrac{-(x-23)}{x-8} >0}$

Divide by - 1 both side :

$\displaystyle{\dfrac{(x-23)}{x-8} <0}$

x - 23 < 0

x < 23

x - 8 < 0

x < 8

x € ( 8 , 23 ) .

Since there is no any common solution set.

Hence , final answer is No solution.