Question 117483


{{{3x<=7x+20}}} Start with the given inequality




{{{3x-7x<=20}}} Subtract 7x from both sides



{{{-4x<=20}}} Combine like terms on the left side



{{{x>=(20)/(-4)}}} Divide both sides by -4 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) 




{{{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,-15,5)}}} 


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



{{{number_line(500,-15,5, -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 right of the point {{{x=-5}}} like this:

{{{drawing(500,50,-15,5,-10,10,
number_line(500,-15,5, -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.