Question 127513


{{{x+5>-13}}} Start with the given inequality




{{{x>-13-5}}}Subtract 5 from both sides



{{{x>-18}}} Combine like terms on the right side


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Answer:

So our answer is {{{x>-18}}} 






Now let's graph the solution set



Start with the given inequality:


{{{x>-18}}}


Set up a number line:

{{{number_line(500,-28,-8)}}} 


Now plot the point {{{x=-18}}} on the number line



{{{number_line(500,-28,-8, -18)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x>-18}}}



{{{0>-18}}} Plug in {{{x=0}}}



Since this inequality is true, we simply shade the entire portion in which contains the point x=0 using the point {{{x=-18}}} as the boundary.This means we shade everything to the right of the point {{{x=-18}}} like this:

{{{drawing(500,50,-28,-8,-10,10,
number_line(500,-28,-8),
circle(-18,-5.8,0.35),
circle(-18,-5.8,0.4),
circle(-18,-5.8,0.45),
blue(line(-18,-5,-18+10,-5)),
blue(line(-18,-6,-18+10,-6)),
blue(line(-18,-7,-18+10,-7)),
blue(arrow(-18,-5,-18+10.2,-5)),
blue(arrow(-18,-5.5,-18+10.2,-5.5)),
blue(arrow(-18,-6,-18+10.2,-6))
)}}}  Graph of {{{x>-18}}} with the shaded region in blue

note: at the point {{{x=-18}}}, there is an <font size=4><b>open</b></font> circle. This means the point {{{x=-18}}} is excluded from the solution set.