Question 128595
{{{4x>7x+20}}} Start with the given inequality




{{{4x-7x>20}}} Subtract 7x from both sides



{{{-3x>20}}} Combine like terms on the left side



{{{x<(20)/(-3)}}} Divide both sides by -3 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) 




{{{x<-20/3}}} Reduce


--------------------------------------------------------------

Answer:

So our answer is {{{x<-20/3}}}  (which is approximately {{{x<-6.667}}} in decimal form)





Now let's graph the solution set



Start with the given inequality:


{{{x<-6.667}}}


Set up a number line:

{{{number_line(500,-16.667,3.333)}}} 


Now plot the point {{{x=-6.667}}} on the number line



{{{number_line(500,-16.667,3.333, -6.667)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x<-6.667}}}



{{{0<-6.667}}} 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=-6.667}}} as the boundary. This means we shade everything to the left of the point {{{x=-6.667}}} like this:

{{{drawing(500,50,-16.667,3.333,-10,10,
number_line(500,-16.667,3.333),
circle(-6.667,-5.8,0.35),
circle(-6.667,-5.8,0.4),
circle(-6.667,-5.8,0.45),
blue(line(-6.667,-5,-6.667-10,-5)),
blue(line(-6.667,-6,-6.667-10,-6)),
blue(line(-6.667,-7,-6.667-10,-7)),
blue(arrow(-6.667,-5,-6.667-10.2,-5)),
blue(arrow(-6.667,-5.5,-6.667-10.2,-5.5)),
blue(arrow(-6.667,-6,-6.667-10.2,-6))
)}}}  Graph of {{{x<-6.667}}} with the shaded region in blue


note: at the point {{{x=-6.667}}}, there is an <font size=4><b>open</b></font> circle. This means the point {{{x=-6.667}}} is excluded from the solution set.