Question

Which graph shows the solution set of x-9/7x+2<=0

Answer 1

For this case we have the following inequality:
 $\frac{x-9}{7x+2} \leq 0$
 Solving for the numerator we have:
 $x-9 \leq 0$
 $x \leq 9$
 Solving for the denominator we have:
 $7x+2\ \textgreater \ 0$
 $7x\ \textgreater \ -2$
 $x \ \textgreater \ \frac{-2}{7}$
 Therefore, the solution is given by:
 $\frac{-2}{7} \ \textless \ x \leq 9$
 The graph that shows this solution is the graphic number 3.
 Answer:
 option 3

Answer 2

We have that
(x-9)/(7x+2)<=0

we know that
the denominator cannot be zero, therefore the value of x = -2 /7 cannot belong to the domain of the function
7x+2=0-----> x=-2/7-----> x=-0.29

using a graph tool
see the attached figure

the solution is the interval
(-2/7, 9]---------> (-0.29, 9]
the value of -0.29 is not included in the solution

therefore 
the answer is the third option