Question 202102
{{{(y - 3)/3 > 1/3 - (y - 5)/6}}} Start with the given inequality



{{{cross(6)^2((y - 3)/cross(3)) > cross(6)^2(1/cross(3)) - cross(6)((y - 5)/cross(6))}}} Multiply EVERY term outside the parenthesis by the LCD 6 to clear out the fractions.



{{{2(y-3)>2(1)-(y-5)}}} Simplify



{{{2(y-3)>2-(y-5)}}} Multiply



{{{2y-6>2-y+5}}} Distribute.



{{{2y-6>-y+7}}} Combine like terms on the right side.



{{{2y>-y+7+6}}} Add {{{6}}} to both sides.



{{{2y+y>7+6}}} Add {{{y}}} to both sides.



{{{3y>7+6}}} Combine like terms on the left side.



{{{3y>13}}} Combine like terms on the right side.



{{{y>(13)/(3)}}} Divide both sides by {{{3}}} to isolate {{{y}}}. 



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Answer:


So the solution is {{{y>13/3}}} 



So the answer in interval notation is   <font size="8">(</font>*[Tex \LARGE \frac{13}{3},\infty]<font size="8">)</font>