Question 146612

{{{5y-2<7y-3}}} Start with the given inequality.



{{{5y<7y-3+2}}} Add {{{2}}} to both sides.



{{{5y-7y<-3+2}}} Subtract {{{7y}}} from both sides.



{{{-2y<-3+2}}} Combine like terms on the left side.



{{{-2y<-1}}} Combine like terms on the right side.



{{{y>(-1)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{y}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{y>1/2}}} Reduce.



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Answer:


So the answer is {{{y>1/2}}} 



Which approximates to {{{y>0.5}}} 




So the answer in set-builder notation is  *[Tex \LARGE \left\{y\|y>\frac{1}{2}\right\}]