SOLUTION: Solve this inequality to describe all possible values of x: {{{ 3/x > 4/x }}} I have not yet had an inequality with a variable on both sides, so am stuck. I have multipl

Algebra ->  Inequalities -> SOLUTION: Solve this inequality to describe all possible values of x: {{{ 3/x > 4/x }}} I have not yet had an inequality with a variable on both sides, so am stuck. I have multipl      Log On


   

Question 200540: Solve this inequality to describe all possible values of x:
+3%2Fx+%3E+4%2Fx+
I have not yet had an inequality with a variable on both sides, so am stuck. I have multiplied both sides by x but do not know where to go from here:
+3x+%3E+4x+ Am I on the right track?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In this case, you can solve this problem the following way...


+3%2Fx+%3E+4%2Fx+ Start with the given inequality.


3x%3E4x Cross multiply


3x-4x%3E0 Subtract 4x from both sides.


-x%3E0 Combine like terms on the left side.


x%3C%280%29%2F%28-1%29 Divide both sides by -1 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3C0 Reduce.


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Answer:

So the solution is x%3C0




So the answer in interval notation is


Also, the answer in set-builder notation is


Here's the graph of the solution set