Question

9 is less than or equal to 6-x<12

Answer 1

You want to solve this? :
9 <= 6-x < 12
??

Answer 2

Yes!

Answer 3

We want to isolate that x in the middle...that is, get it alone in there. Get rid of that 6 by subtracting 6 from all 3 places...the left, the middle and the right. What do you get?

Answer 4

9 - 6 <= 6 - x - 6 < 12 - 6
What do you get when you simplify that?

Answer 5

3<=-x<6

Answer 6

Correct.
Now, how do we get rid of that - next to the x?
Multiply left, center and right by -1 is the easiest way.
But remember that when you multiply inequalities by negatives you have to change their directions: <= becomes >= and < becomes >

Answer 7

What does the equation look like now?

Answer 8

Please tell me what you did not understand in my last post.
Take your 3<=-x<6 and follow my instructions, but please let me know if there is a line you don't understand.

Answer 9

-3<x>-6

Answer 10

Your numbers look good, but one of your symbols need fixing. All you have to do is change the direction of the symbols. Right becomes left, left becomes right.
The answer is -3 >= x > -6