Answer:
The inequality describes all possible value of x is 14 < x < 32 ⇒ D
Step-by-step explanation:
In any triangle:
- The sum of the lengths of any two sides must be greater than the length of the 3rd side
- The length of any side must greater than the difference of the lengths of the other two sides
- The difference of the other sides < The side < The sum of the other sides
In the given figure
∵ ABC is a triangle
∵ AC = 9 and BC = 21
∵ AB is the third side of the triangle
→ By using the rules above
∴ BC - AC < AB < BC + AC
∵ AB = x - 2
→ Substitute their values in the inequality above
∵ 21 - 9 < x - 2 < 21 + 9
∴ 12 < x - 2 < 30
→ Add 2 to the 3 terms
∴ 12 + 2 < x - 2 + 2 < 30 + 2
∴ 14 < x < 32
∴ The inequality describes all possible value of x is 14 < x < 32
