Question 101071
Start with the given inequality:


{{{y>3}}}


Set up a number line:

{{{number_line(500,-7,13)}}} note: just replace the x with the variable you are working with



Now plot the point y=3 on the number line



{{{number_line(500,-7,13, 3)}}}



Now pick any test point you want, I'm going to choose y=0, and test the inequality {{{y>3}}}



{{{0>3}}} 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=3 as the boundary. This means we shade everything to the right of the point y=3 like this:

{{{drawing(500,50,-7,13,-10,10,
number_line(500,-7,13),
circle(3,-5.8,0.35),
circle(3,-5.8,0.4),
circle(3,-5.8,0.45),
blue(line(3,-5,3+10,-5)),
blue(line(3,-6,3+10,-6)),
blue(line(3,-7,3+10,-7)),
blue(arrow(3,-5,3+10.2,-5)),
blue(arrow(3,-5.5,3+10.2,-5.5)),
blue(arrow(3,-6,3+10.2,-6))
)}}}  Graph of {{{y>3}}} with the shaded region in blue

note: at the point y=3, there is an <font size=4><b>open</b></font> circle. This means the point y=3 is excluded from the solution set.