12≥−x+9and

6≤−x+9

To solve the inequalities, we will isolate x in each inequality.

For 12 ≥ -x + 9, we will first subtract 9 from both sides:
12 - 9 ≥ -x + 9 - 9
3 ≥ -x

Since we want x to be positive, we can multiply both sides of the inequality by -1, which changes the direction of the inequality:
-3 ≤ x

For 6 ≤ -x + 9, we will first subtract 9 from both sides:
6 - 9 ≤ -x + 9 - 9
-3 ≤ -x

Since we want x to be positive, we can multiply both sides of the inequality by -1, which changes the direction of the inequality:
3 ≥ x

Therefore, the solution for both inequalities is:
-3 ≤ x ≤ 3