Question

Solve the following inequality algebraically. |x-9|>=2

Answer 1

To solve the inequality |x-9|>=2 algebraically, consider two cases: x-9>=2 and -(x-9)>=2. Combining the two cases, the solution to the inequality is x<=7 or x>=11.

Step-by-step explanation:

To solve the inequality |x-9|>=2 algebraically, we have to consider two cases:

1. Case 1: x-9>=2
2. Case 2: -(x-9)>=2

In Case 1, we have x-9>=2. Adding 9 to both sides, we get x>=11.

In Case 2, we have -(x-9)>=2. Multiplying both sides by -1 and simplifying, we get x<=7.

Combining the two cases, we have x<=7 or x>=11 as the solution to the inequality.