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)