Question

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

Answer 1

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

Answer 2

For this case we have the following inequality:

`(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 \ (-2)/(7)`
Therefore, the solution is given by:

`(-2)/(7) \ \textless \ x \leq 9`
The graph that shows this solution is the graphic number 3.
Answer:
option 3