Question 220537
{{{7y-12<8y+15}}} Start with the given inequality.



{{{7y<8y+15+12}}} Add {{{12}}} to both sides.



{{{7y-8y<15+12}}} Subtract {{{8y}}} from both sides.



{{{-y<15+12}}} Combine like terms on the left side.



{{{-y<27}}} Combine like terms on the right side.



{{{y>(27)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{y>-27}}} Reduce.



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Answer:


So the solution is {{{y>-27}}}



So the answer in interval notation is *[Tex \LARGE \left(-27,\infty\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{y\|y>-27\right\}]



Here's the graph of the solution set on a number line:


{{{drawing(500,80,-37, -17,-10, 10,
number_line( 500, -37, -17),

arrow(-27,0,-17,0),
arrow(-27,0.30,-17,0.30),
arrow(-27,0.15,-17,0.15),
arrow(-27,-0.15,-17,-0.15),
arrow(-27,-0.30,-17,-0.30),

circle(-27,0,0.3),
circle(-27,0,0.3),
circle(-27,0,0.3),
circle(-27,0,0.3-0.02)
)}}}


Note: there is an open circle at the endpoint.