Question 743489
{{{(5x+2)/(3x-1)<4}}}

{{{(5x+2)/(3x-1)-4<0}}}

{{{(5x+2)/(3x-1)-4(3x-1)/(3x-1)<0}}}

{{{((5x+2)-12x+4)/(3x-1)<0}}}

{{{(6-7x)/(3x-1)}}}


Next we test on the intervals that our boundary values generated:

First interval:
{{{-infinity<x<1/3}}}

Suppose x=0
then our inequality gives us 

{{{-2<4}}} <---TRUE!
 

Second interval:
{{{1/3<x<6/7}}}


Suppose x=0.5
then our inequality gives us 

{{{9<4}}} <---False!

Third interval: 
{{{6/7<x<infinity}}}


Suppose x=1
then our inequality gives us 

{{{7/2<4}}} <---TRUE!


solution:

{{{-infinity<x<1/3}}} union {{{6/7<x<infinity}}}