Question 103723
Start with the given inequality:


{{{x>1}}}


Set up a number line:

{{{number_line(500,-9,11)}}} 


Now plot the point x=1 on the number line



{{{number_line(500,-9,11, 1)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x>1}}}



{{{0>1}}} 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=1 as the boundary. This means we shade everything to the right of the point x=1 like this:

{{{drawing(500,50,-9,11,-10,10,
number_line(500,-9,11),
circle(1,-5.8,0.35),
circle(1,-5.8,0.4),
circle(1,-5.8,0.45),
blue(line(1,-5,1+10,-5)),
blue(line(1,-6,1+10,-6)),
blue(line(1,-7,1+10,-7)),
blue(arrow(1,-5,1+10.2,-5)),
blue(arrow(1,-5.5,1+10.2,-5.5)),
blue(arrow(1,-6,1+10.2,-6))
)}}}  Graph of {{{x>1}}} with the shaded region in blue

note: at the point x=1, there is an <font size=4><b>open</b></font> circle. This means the point x=1 is excluded from the solution set.