Question 96854


{{{-3a+10<-11}}} Start with the given  inequality



{{{-3a<-11-10}}}Subtract 10 from both sides



{{{-3a<-21}}} Combine like terms on the right side



{{{a>(-21)/(-3)}}} Divide both sides by -3 to isolate a  (note: dividing by both sides by a negative number flips the inequality sign)




{{{a>7}}} Divide


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

Answer:

So our answer is {{{a>7}}} 




Now let's graph the solution





Start with the given inequality:


{{{a>7}}}


Set up a number line:

{{{number_line(500,-3,17)}}} note: just replace the x with the variable you are working with



Now plot the point a=7 on the number line



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



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



{{{0>7}}} Plug in {{{a=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 a=0 using the point a=7 as the boundary. This means we shade everything to the right of the point a=7 like this:

{{{drawing(500,50,-3,17,-10,10,
number_line(500,-3,17),
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 {{{a>7}}} with the shaded region in blue

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