Answer:
x<-8 or x>1/5
Step-by-step explanation:
[tex]\frac{x+8}{5x-1} >0[/tex]
First we replace > symbol by = sign
[tex]\frac{x+8}{5x-1} =0[/tex]
To solve for x we multiply 5x-1 on both sides
x+8 =0
x=-8
5x-1=0 solve for x
x= 1/5
WE got two values x=-8 and x= 1/5
Now we make a number line and check with each interval
x<-8, -8<x<1/5, x>1/5
Pick x= -9 and check with the given inequality
[tex]\frac{-9+8}{5(-9)-1} >0[/tex]
1/46 >0 is true, so x<-8 satisfies our inequality
Pick x= 0 and check with the given inequality
[tex]\frac{0+8}{5(0)-1} >0[/tex]
-8 >0 is false , -8<x<1/5 does not satifies our inequality
Pick x= 2 and check with the given inequality
[tex]\frac{2+8}{5(2)-1} >0[/tex]
10/9>0 is true , x>1/5 satisfies our inequality
