Question 113924
Start with the given inequality:


{{{x<=0}}}


Set up a number line and plot the point {{{x=0}}} on the number line



{{{number_line(500,-10,10, 0)}}}



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



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

{{{drawing(500,50,-10,10,-10,10,
number_line(500,-10,10, 0),
blue(line(0,-5,0-10,-5)),
blue(line(0,-6,0-10,-6)),
blue(line(0,-7,0-10,-7)),
blue(arrow(0,-5,0-10.2,-5)),
blue(arrow(0,-5.5,0-10.2,-5.5)),
blue(arrow(0,-6,0-10.2,-6))
)}}}  Graph of {{{x<=0}}} with the shaded region in blue

note: at the point {{{x=0}}}, there is an <font size=4><b>closed</b></font> circle. This means the point {{{x=0}}} is included from the solution set.