Question 102505
Start with the given inequality:


{{{x<-3}}}


Set up a number line:

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


Now plot the point x=-3 on the number line



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



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



{{{0<-3}}} Plug in {{{x=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 x=0 using the point x=-3 as the boundary. This means we shade everything to the left of the point x=-3 like this:

{{{drawing(500,50,-13,7,-10,10,
number_line(500,-13,7),
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 {{{x<-3}}} with the shaded region in blue


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