Question 558142
<pre>
{{{x/5}}} < {{{3/(6x-1)}}}

{{{x/5}}} - {{{3/(6x-1)}}} < 0

The LCD = 5(6x-1)

{{{x/5}}}·{{{(6x-1)/(6x-1)}}} - {{{3/(6x-1)}}}·{{{5/5}}} < 0

{{{(6x^2-x)/(5(6x-1))}}} - {{{15/(5(6x-1))}}} < 0

{{{(6x^2-x-15)/(5(6x-1))}}} < 0

{{{((3x-5)(2x+3))/(5(6x-1))}}} < 0

"< 0" means negative, so we want the left side to be negative.

Find the critical values by setting numerator = 0 and
denominator = 0
                 
There are 3 critical numbers, {{{5/3}}}, {{{-3/2}}}, and {{{1/6}}}

In mixed fractions, they are {{{1&2/3}}}, {{{-1&1/2}}}, and {{{1/6}}}

We make this chart

 {{{matrix(6,7,

Interval,   "|" , x<-1&1/2, "|", 1/6<x<1&2/3, "|", x>1&2/3, 
Test_Value, "|",     -2   , "|",     1,      "|",     2,                     
Sign_of_(3x-5),"|",   ""-"" , "|",     ""-"",  "|",    ""+"",     
Sign_of_(2x+3),"|",   ""-"" , "|",     ""+"",  "|",    ""+"",
Sign_of_5(6x-1),"|",   ""-"" , "|",     ""+"",  "|",    ""+"",
Sign_of_left_side, "|",   ""-"" , "|",     ""-"",  "|",    ""+"")}}}

The left side is negative on the intervals {{{x<-1&1/2}}}, and {{{1/6<x<1&2/3}}}

{{{(matrix(1,3,-infinity, ",", -1&1/2))}}} U {{{(matrix(1,3,1/6,",",1&2/3))}}}

Edwin</pre>