Question 105326
Which one is it? I'm assuming you want to solve the first inequality


{{{3+x<-4}}} Start with the given inequality



{{{x<-4-3}}}Subtract 3 from both sides



{{{x<-7}}} Combine like terms on the right side



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Answer:

So our answer is {{{x<-7}}} 




Now let's graph the solution set



Start with the given inequality:


{{{x<-7}}}


Set up a number line:

{{{number_line(500,-17,3)}}} 


Now plot the point x=-7 on the number line



{{{number_line(500,-17,3, -7)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x<-7}}}



{{{0<-7}}} 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=-7 as the boundary. This means we shade everything to the left of the point x=-7 like this:

{{{drawing(500,50,-17,3,-10,10,
number_line(500,-17,3),
circle(-7,-5.8,0.35),
circle(-7,-5.8,0.4),
circle(-7,-5.8,0.45),
blue(line(-7,-5,-7-10,-5)),
blue(line(-7,-6,-7-10,-6)),
blue(line(-7,-7,-7-10,-7)),
blue(arrow(-7,-5,-7-10.2,-5)),
blue(arrow(-7,-5.5,-7-10.2,-5.5)),
blue(arrow(-7,-6,-7-10.2,-6))
)}}}  Graph of {{{x<-7}}} with the shaded region in blue


note: at the point x=-7, there is an <font size=4><b>open</b></font> circle. This means the point x=-7 is excluded from the solution set.