Solve the inequality and express your answer in interval notation. if u answer correctly 50 points

For the interval
x≤−6:

Then we pick
x=−7. Then,

(−7−5)(−7+6)
≥0.
After simplifying, we get
−1.2≥0, which is false.
Drop this interval..

For the interval
−6≤x≤3:

Let's pick

x=0. Then,

(0−5)(0+6) ≥0.
After simplifying, we get

10≥0, which is true.
Keep this interval..

For the interval
3≤x≤5:

Let's pick

x=4. Then,

(4−5)(4+6) ≥0.
After simplifying, we get
−10≥0, which is false.
Drop this interval..

For the interval
x≥5:

Then we pick
x=6. Then,

6−3

(6−5)(6+6)
≥0.
After simplifying, we get

4≥0, which is true.
Keep this interval..


Notice the equation contains
x-3
x−3 in the denominator. Since any denominator must not equal zero, the domain is restricted to
x−3≠0. Solving for
x, we have:
x≠3

Add the domain restrictions:(answer)

−6≤x<3
x≥5

(I couldn’t fit everything in)