Question 107459

{{{2y+7>11}}} Start with the given inequality



{{{2y>11-7}}}Subtract 7 from both sides



{{{2y>4}}} Combine like terms on the right side



{{{y>(4)/(2)}}} Divide both sides by 2 to isolate y 




{{{y>2}}} Divide


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

Answer:

So our answer is {{{y>2}}}



Now let's graph the solution set 



Start with the given inequality:


{{{y>2}}}


Set up a number line:

{{{number_line(500,-8,12)}}} note: just replace the x with the variable you are working with



Now plot the point {{{y=2}}} on the number line



{{{number_line(500,-8,12, 2)}}}



Now pick any test point you want, I'm going to choose y=0, and test the inequality {{{y>2}}}



{{{0>2}}} Plug in {{{y=0}}}



Since this inequality is <font size=4><b>not</b></font> true, we simply shade the entire portion that does <font size=4><b>not</b></font> contain the point y=0 using the point {{{y=2}}} as the boundary. This means we shade everything to the right of the point {{{y=2}}} like this:

{{{drawing(500,50,-8,12,-10,10,
number_line(500,-8,12),
circle(2,-5.8,0.35),
circle(2,-5.8,0.4),
circle(2,-5.8,0.45),
blue(line(2,-5,2+10,-5)),
blue(line(2,-6,2+10,-6)),
blue(line(2,-7,2+10,-7)),
blue(arrow(2,-5,2+10.2,-5)),
blue(arrow(2,-5.5,2+10.2,-5.5)),
blue(arrow(2,-6,2+10.2,-6))
)}}}  Graph of {{{y>2}}} with the shaded region in blue

note: at the point {{{y=2}}}, there is an <font size=4><b>open</b></font> circle. This means the point {{{y=2}}} is excluded from the solution set.