Question 127333


Now let's graph the solution set



Start with the given inequality:


{{{x<2}}}


Set up a number line:

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


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



{{{number_line(500,-8,12, 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 true, we simply shade the entire portion in which contains 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,-8,12,-10,10,
number_line(500,-8,12),
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.