Question 117754


{{{y-3>=5}}} Start with the given inequality




{{{y>=5+3}}}Add 3 to both sides



{{{y>=8}}} Combine like terms on the right side


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Answer:

So our answer is {{{y>=8}}} 








Now let's graph the solution set



Start with the given inequality:


{{{y>=8}}}


Set up a number line:

{{{number_line(500,-2,18)}}} note: just replace the x with the variable you are working with



Now plot the point {{{y=8}}} on the number line



{{{number_line(500,-2,18, 8)}}}



Now pick any test point you want, I'm going to choose y=0, and test the inequality {{{y>=8}}}



{{{0>=8}}} 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=8}}} as the boundary. This means we shade everything to the right of the point {{{y=8}}} like this:

{{{drawing(500,50,-2,18,-10,10,
number_line(500,-2,18, 8),
blue(line(8,-5,8+10,-5)),
blue(line(8,-6,8+10,-6)),
blue(line(8,-7,8+10,-7)),
blue(arrow(8,-5,8+10.2,-5)),
blue(arrow(8,-5.5,8+10.2,-5.5)),
blue(arrow(8,-6,8+10.2,-6))
)}}} Graph of {{{y>=8}}} with the shaded region in blue

note: at the point {{{y=8}}}, there is an <font size=4><b>closed</b></font> circle. This means the point {{{y=8}}} is included from the solution set.