Question 118333

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




{{{cross(4)(-x/cross(4))=(4)(3)}}} Multiply both sides by 4.



{{{-x=12}}} Multiply




{{{x<(12)/(-1)}}} Divide both sides by -1 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) 




{{{x<-12}}} Divide


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Answer:

So our answer is {{{x<-12}}} 




Now let's graph the solution set



Start with the given inequality:


{{{x<-12}}}


Set up a number line:

{{{number_line(500,-22,-2)}}} 


Now plot the point {{{x=-12}}} on the number line



{{{number_line(500,-22,-2, -12)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x<-12}}}



{{{0<-12}}} 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=-12}}} as the boundary. This means we shade everything to the left of the point {{{x=-12}}} like this:

{{{drawing(500,50,-22,-2,-10,10,
number_line(500,-22,-2),
circle(-12,-5.8,0.35),
circle(-12,-5.8,0.4),
circle(-12,-5.8,0.45),
blue(line(-12,-5,-12-10,-5)),
blue(line(-12,-6,-12-10,-6)),
blue(line(-12,-7,-12-10,-7)),
blue(arrow(-12,-5,-12-10.2,-5)),
blue(arrow(-12,-5.5,-12-10.2,-5.5)),
blue(arrow(-12,-6,-12-10.2,-6))
)}}}  Graph of {{{x<-12}}} with the shaded region in blue


note: at the point {{{x=-12}}}, there is an <font size=4><b>open</b></font> circle. This means the point {{{x=-12}}} is excluded from the solution set.