Question 125398


{{{5x<=25}}} Start with the given inequality




{{{x<=(25)/(5)}}} Divide both sides by 5 to isolate x 




{{{x<=5}}} Divide


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Answer:

So our answer is {{{x<=5}}} 




Now let's graph the solution set



Start with the given inequality:


{{{x<=5}}}


Set up a number line:

{{{number_line(500,-5,15)}}} 


Now plot the point {{{x=5}}} on the number line



{{{number_line(500,-5,15, 5)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x<=5}}}



{{{0<=5}}} 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=5}}} as the boundary.This means we shade everything to the left of the point {{{x=5}}} like this:

{{{drawing(500,50,-5,15,-10,10,
number_line(500,-5,15, 5),
blue(line(5,-5,5-10,-5)),
blue(line(5,-6,5-10,-6)),
blue(line(5,-7,5-10,-7)),
blue(arrow(5,-5,5-10.2,-5)),
blue(arrow(5,-5.5,5-10.2,-5.5)),
blue(arrow(5,-6,5-10.2,-6))
)}}}  Graph of {{{x<=5}}} with the shaded region in blue

note: at the point {{{x=5}}}, there is an <font size=4><b>closed</b></font> circle. This means the point {{{x=5}}} is included from the solution set.