Question 147109

{{{3y-3<5y-4}}} Start with the given inequality.



{{{3y<5y-4+3}}} Add {{{3}}} to both sides.



{{{3y-5y<-4+3}}} Subtract {{{5y}}} from both sides.



{{{-2y<-4+3}}} 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 interval notation is *[Tex \LARGE \left(\frac{1}{2},\infty\right)]



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


Here's the graph of the solution set


{{{drawing(500,80,-9, 11,-10, 10,
number_line( 500, -9, 11),

arrow(1/2,0,11,0),
arrow(1/2,0.30,11,0.30),
arrow(1/2,0.15,11,0.15),
arrow(1/2,-0.15,11,-0.15),
arrow(1/2,-0.30,11,-0.30),

circle(1/2,0,0.3),
circle(1/2,0,0.3),
circle(1/2,0,0.3),
circle(1/2,0,0.3-0.02)
)}}}



Note: there is an <b>open</b> circle at {{{y=1/2}}} which means that we're excluding that value from the solution set.