Solve the inequality and express your answer in interval notation

The number line graph is also attached below.

Step-by-step explanation:

Given the inequality

Let's find the critical points of the inequality.

       (Multiply both sides by x-3)

   (Factor left side of equation)

or    (Set factors equal to 0)

or

Check possible critical points.

x = 5  (Works in original equation)

x = −6  (Works in original equation)

Critical points:

x = 5 or x = −6      (Makes both sides equal)

x = 3          (Makes left denominator equal to 0)

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x ≤ −6     (Doesn't work in original inequality)

−6 ≤ x < 3      (Works in original inequality)

3 < x ≤ 5         (Doesn't work in original inequality)

x ≥ 5 (Works in original inequality)

so

Therefore,

The number line graph is also attached below.