Question 126118


Now let's graph the solution set



Start with the given inequality:


{{{x < -2}}}


Set up a number line:

{{{number_line(500,-12,8)}}} 


Now plot the point {{{x = -2}}} on the number line



{{{number_line(500,-12,8,  -2)}}}



Now pick any test point you want, I'm going to choose x =0, and test the inequality {{{x < -2}}}



{{{0< -2}}} 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 = -2}}} as the boundary. This means we shade everything to the left of the point {{{x = -2}}} like this:

{{{drawing(500,50,-12,8,-10,10,
number_line(500,-12,8),
circle( -2,-5.8,0.35),
circle( -2,-5.8,0.4),
circle( -2,-5.8,0.45),
blue(line( -2,-5, -2-10,-5)),
blue(line( -2,-6, -2-10,-6)),
blue(line( -2,-7, -2-10,-7)),
blue(arrow( -2,-5, -2-10.2,-5)),
blue(arrow( -2,-5.5, -2-10.2,-5.5)),
blue(arrow( -2,-6, -2-10.2,-6))
)}}}  Graph of {{{x < -2}}} with the shaded region in blue


note: at the point {{{x = -2}}}, there is an <font size=4><b>open</b></font> circle. This means the point {{{x = -2}}} is excluded from the solution set.