Question 643496
I need some help solving this inequality.

{{{x-5/3-x}}}<0

Thank you so much!


Before trying to solve this inequality, upon observing it, we realize that whatever x-value one uses, that x-value becomes 0. This is because we are adding x, and also subtracting it (see inequality). This leaves us with: {{{- 5/3 < 0}}}, which is always, and will forever be TRUE. This means that ANY x-value inserted into the inequality will satisfy it (make it true). 


Anyway, still working the problem out, we convert the left-side expression to one with a common denominator, 3 to get:


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


{{{- 5/3 < 0}}} ----- 3x - 3x in numerator equals 0
 

Since this is always true, ANY value that is plugged in for x will satisfy the inequality, thereby leading to the solution x = ALL REALS.


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