Question 117756


{{{2x+7>5}}} Start with the given inequality




{{{2x>5-7}}}Subtract 7 from both sides



{{{2x>-2}}} Combine like terms on the right side



{{{x>(-2)/(2)}}} Divide both sides by 2 to isolate x 




{{{x>-1}}} Divide


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Answer:

So our answer is {{{x>-1}}} 







Now let's graph the solution set



Start with the given inequality:


{{{x>-1}}}


Set up a number line:

{{{number_line(500,-11,9)}}} 


Now plot the point {{{x=-1}}} on the number line



{{{number_line(500,-11,9, -1)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x>-1}}}



{{{0>-1}}} 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=-1}}} as the boundary.This means we shade everything to the right of the point {{{x=-1}}} like this:

{{{drawing(500,50,-11,9,-10,10,
number_line(500,-11,9),
circle(-1,-5.8,0.35),
circle(-1,-5.8,0.4),
circle(-1,-5.8,0.45),
blue(line(-1,-5,-1+10,-5)),
blue(line(-1,-6,-1+10,-6)),
blue(line(-1,-7,-1+10,-7)),
blue(arrow(-1,-5,-1+10.2,-5)),
blue(arrow(-1,-5.5,-1+10.2,-5.5)),
blue(arrow(-1,-6,-1+10.2,-6))
)}}}  Graph of {{{x>-1}}} with the shaded region in blue

note: at the point {{{x=-1}}}, there is an <font size=4><b>open</b></font> circle. This means the point {{{x=-1}}} is excluded from the solution set.