Solve the following inequality. 50x-75<50/x

Question

Solve the following inequality. 50x-75<50/x?

 

 

Is the point x=0 included in the solution set of the inequality?

Are the other finite end points of the intervals included in the solution set?

What is the solution set?

Answer 1

50x-75<50/x

multiply both sides by x

50x^2-75x<50

50x^2-75x-50<0

divide all terms by 25

2x^2-3x-2<0

factor

(2x+1)(x-2)<0

2x+1<0

2x<-1

x<-1/2

x-2<0

x<2

solution set: x<-1/2 or 0<x<2 (x≠0 because 50/x would be undefined)