Question 200540
In this case, you can solve this problem the following way...



{{{ 3/x > 4/x }}} Start with the given inequality.



{{{3x>4x}}} Cross multiply



{{{3x-4x>0}}} Subtract {{{4x}}} from both sides.



{{{-x>0}}} Combine like terms on the left side.



{{{x<(0)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<0}}} Reduce.



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Answer:


So the solution is {{{x<0}}} 





So the answer in interval notation is *[Tex \LARGE \left(-\infty,0\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x<0\right\}]



Here's the graph of the solution set


{{{drawing(500,80,-10, 10,-10, 10,
number_line( 500, -10, 10),


arrow(0,0,-10,0),
arrow(0,0.30,-10,0.30),
arrow(0,0.15,-10,0.15),
arrow(0,-0.15,-10,-0.15),
arrow(0,-0.30,-10,-0.30),




circle(0,0,0.3),
circle(0,0,0.3),
circle(0,0,0.3),
circle(0,0,0.3-0.02)
)}}}