Question 125919
Simply solve each inequality individually and the final solution will be the union of these two solutions


{{{x + 4 < 0}}}} Start with the first inequality



{{{x<0-4}}}Subtract 4 from both sides



{{{x<-4}}} Combine like terms on the right side




So the first part of our answer is {{{x<-4}}} 




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{{{6x > -12}}}} Start with the second inequality




{{{x>(-12)/(6)}}} Divide both sides by 6 to isolate x 




{{{x>-2}}} Divide




So the second part of the answer is {{{x>-2}}}  




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Answer:


So together the solution is 


{{{x<-4}}} or {{{x>-2}}}




So the solution in interval notation is 


*[Tex \LARGE \left(-\infty,-4\right) \cup \left(-2,\infty)]





Now let's graph the solution set


{{{drawing(500,50,-14,6,-10,10,
number_line(500,-14,6),
circle(-4,-5.8,0.35),
circle(-4,-5.8,0.4),
circle(-4,-5.8,0.45),
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)),

circle(-2,-5.8,0.35),
circle(-2,-5.8,0.4),
circle(-2,-5.8,0.45),
blue(line(-2,-5,-2+10,-5)),
blue(line(-2,-6,-2+10,-6)),
blue(line(-2,-7,-2+10,-7)),
blue(arrow(-2,-5,-2+8.2,-5)),
blue(arrow(-2,-5.5,-2+8.2,-5.5)),
blue(arrow(-2,-6,-2+8.2,-6))

)}}}  Graph of {{{x<-4}}} (left sided blue region) and {{{x>-2}}} (right sided blue region)