Question 134286


{{{7x>=28}}} Start with the given inequality




{{{x>=(28)/(7)}}} Divide both sides by 7 to isolate x 




{{{x>=4}}} Divide


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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,-6,14)}}} 


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



{{{number_line(500,-6,14, 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 <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=4}}} as the boundary. This means we shade everything to the right of the point {{{x=4}}} like this:

{{{drawing(500,50,-6,14,-10,10,
number_line(500,-6,14, 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.