Question 117700


{{{3x>=2x-4}}} Start with the given inequality




{{{3x-2x>=-4}}} Subtract 2x from both sides



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


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Answer:

So our answer is {{{x>=-4}}} 





Now let's graph the solution set



Start with the given inequality:


{{{x>=-4}}}


Set up a number line:

{{{number_line(500,-14,6)}}} 


Now plot the point {{{x=-4}}} on the number line



{{{number_line(500,-14,6, -4)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x>=-4}}}



{{{0>=-4}}} 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=-4}}} as the boundary.This means we shade everything to the right of the point {{{x=-4}}} like this:

{{{drawing(500,50,-14,6,-10,10,
number_line(500,-14,6, -4),
blue(line(-4,-5,-4+10,-5)),
blue(line(-4,-6,-4+10,-6)),
blue(line(-4,-7,-4+10,-7)),
blue(arrow(-4,-5,-4+10.2,-5)),
blue(arrow(-4,-5.5,-4+10.2,-5.5)),
blue(arrow(-4,-6,-4+10.2,-6))
)}}} Graph of {{{x>=-4}}} with the shaded region in blue

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