Question 115218
{{{-x<=91}}} Start with the given inequality




{{{x>=(91)/(-1)}}} Divide both sides by -1 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) 




{{{x>=-91}}} Divide


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Answer:

So our answer is {{{x>=-91}}} 



Now let's graph the solution



Start with the given inequality:


{{{x>=-91}}}


Set up a number line:

{{{number_line(500,-101,-81)}}} 


Now plot the point {{{x=-91}}} on the number line



{{{number_line(500,-101,-81, -91)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x>=-91}}}



{{{0>=-91}}} 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=-91}}} as the boundary.This means we shade everything to the right of the point {{{x=-91}}} like this:

{{{drawing(500,50,-101,-81,-10,10,
number_line(500,-101,-81, -91),
blue(line(-91,-5,-91+10,-5)),
blue(line(-91,-6,-91+10,-6)),
blue(line(-91,-7,-91+10,-7)),
blue(arrow(-91,-5,-91+10.2,-5)),
blue(arrow(-91,-5.5,-91+10.2,-5.5)),
blue(arrow(-91,-6,-91+10.2,-6))
)}}} Graph of {{{x>=-91}}} with the shaded region in blue

note: at the point {{{x=-91}}}, there is an <font size=4><b>closed</b></font> circle. This means the point {{{x=-91}}} is included from the solution set.