Question 127339


Now let's graph the solution set



Start with the given inequality:


{{{x > 3}}}


Set up a number line:

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


Now plot the point {{{x = 3}}} on the number line



{{{number_line(500,-7,13,  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 right of the point {{{x = 3}}} like this:

{{{drawing(500,50,-7,13,-10,10,
number_line(500,-7,13),
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.