Question 92577
Start with the given inequality:


{{{x>=-7}}}


Set up a number line:

{{{number_line( 500, -10, 10)}}} 


Now plot the point x=-7 on the number line



{{{number_line( 500, -10, 10, -7)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x>=-7}}}



{{{0>=-7}}} 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=-7 as the boundary.This means we shade everything to the right of the point x=-7 like this

{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -10, 10, -7),
blue(line(-7,-5,-7+16.8,-5)),
blue(line(-7,-6,-7+16.8,-6)),
blue(line(-7,-7,-7+16.8,-7)),
blue(arrow(-7,-5,-7+17,-5)),
blue(arrow(-7,-5.5,-7+17,-5.5)),
blue(arrow(-7,-6,-7+17,-6))
)}}} Graph of {{{x>=-7}}} with the shaded region in blue

note: at the point x=-7, there is an <b>closed</b> circle. This means the point x=-7 is included from the solution set.