Question 93203
{{{x+11>-5}}} Start with the given equation



{{{x>-5-11}}} Subtract 11 from both sides





{{{x>-16}}} Combine like terms -11 and -5 on the right side to get -16



So our answer is

{{{x> -16}}}


Now lets graph the inequality {{{x> -16}}}



Start with the given inequality:


{{{x>-16}}}


Set up a number line:

{{{number_line(500,-26,-6)}}} 


Now plot the point x=-16 on the number line



{{{number_line(500,-26,-6, -16)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x>-16}}}



{{{0>-16}}} 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=-16 as the boundary.This means we shade everything to the right of the point x=-16 like this

{{{drawing(500,50,-26,-6,-10,10,
number_line(500,-26,-6),
circle(-16,-5.8,0.35),
circle(-16,-5.8,0.4),
circle(-16,-5.8,0.45),
blue(line(-16,-5,-16+10,-5)),
blue(line(-16,-6,-16+10,-6)),
blue(line(-16,-7,-16+10,-7)),
blue(arrow(-16,-5,-16+10.2,-5)),
blue(arrow(-16,-5.5,-16+10.2,-5.5)),
blue(arrow(-16,-6,-16+10.2,-6))
)}}}  Graph of {{{x>-16}}} with the shaded region in blue

note: at the point x=-16, there is an <b>open</b> circle. This means the point x=-16 is excluded from the solution set.