Answer:
x ≤ 10 or x > 12
Explanation:
Will first solve the inequalities to get the interval for x
1 ≥ x -9
First switch sides. When you switch sides the ≥ is reversed to a ≤ inequality
So it is
x - 9 ≤ 1
Adding 9 to both sides gives
x ≤ 10 so that is one inequality
x - 9 > 3
Add 9 to both sides giving
x > 12
Inequality is x ≤ 10 or x > 12
Check attached graph. Not that great but it shows the essentials
Filled circle at 10 shows that 10 is included in the inequality ( ≤ ) and an unfilled circle on 12 shows that 12 is not part of the inequality ( > )