Question 157249
{{{42-13y>15y-19}}} Start with the given inequality.



{{{-13y>15y-19-42}}} Subtract {{{42}}} from both sides.



{{{-13y-15y>-19-42}}} Subtract {{{15y}}} from both sides.



{{{-28y>-19-42}}} Combine like terms on the left side.



{{{-28y>-61}}} Combine like terms on the right side.



{{{y<(-61)/(-28)}}} Divide both sides by {{{-28}}} to isolate {{{y}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{y<61/28}}} Reduce.



----------------------------------------------------------------------


Answer:


So the answer is {{{y<61/28}}} 



Which approximates to {{{y<2.179}}} 





So the answer in interval notation is *[Tex \LARGE \left(-\infty,\frac{61}{28}\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{y\|y<\frac{61}{28}\right\}]




Here's the graph of the solution set


{{{drawing(500,80,-5, 8,-10, 10,
number_line( 500, -5, 8),


arrow(61/28,0,8,0),
arrow(61/28,0.30,8,0.30),
arrow(61/28,0.15,8,0.15),
arrow(61/28,-0.15,8,-0.15),
arrow(61/28,-0.30,8,-0.30),




circle(61/28,0,0.3),
circle(61/28,0,0.3),
circle(61/28,0,0.3),
circle(61/28,0,0.3-0.02)
)}}}



Note: the endpoint is an open circle which excludes the value at that point from the solution set.



Questions? Email me at <a href="mailto:jim_thompson5910@hotmail.com?subject=Algebra Help">jim_thompson5910@hotmail.com</a> (note: the space is really an underscore)