Question 163038
I'm assuming that you want to find the solution set of the system of inequalites {{{-1/3-2x/3>1/3}}} AND {{{-7x-1/2<6&1/2 }}} right?



{{{-1/3-2x/3>1/3}}} Start with the first inequality.



{{{3(-1/cross(3)-2x/cross(3))>3(1/cross(3))}}} Multiply both sides by the LCD {{{3}}} to clear any fractions.



{{{-1-2x>1}}} Distribute and multiply.



{{{-2x>1+1}}} Add {{{1}}} to both sides.



{{{-2x>2}}} Combine like terms on the right side.



{{{x<(2)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<-1}}} Reduce.



So the first part of the answer is {{{x<-1}}}



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{{{-7x-1/2<6&1/2}}} Start with the second inequality



{{{-7x-1/2<13/2}}} Convert the mixed fraction into an improper fraction.



{{{2(-7x-1/cross(2))<2(13/cross(2))}}} Multiply both sides by the LCD {{{2}}} to clear any fractions.



{{{-14x-1<13}}} Distribute and multiply.



{{{-14x<13+1}}} Add {{{1}}} to both sides.



{{{-14x<14}}} Combine like terms on the right side.



{{{x>(14)/(-14)}}} Divide both sides by {{{-14}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>-1}}} Reduce.



So the second part of the answer is {{{x>-1}}}



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Answer:


So together the answers are {{{x<-1}}} AND {{{x>-1}}}


This is NOT possible since you cannot have a number that is both less and greater than some number. It's like saying "pick a number that is BOTH positive AND negative", it's not possible.



So there are no solutions