Which inequality represents the value of x that ensures triangle abc exists?

Option A.

Step-by-step explanation:

According to triangle inequality theorem, a triangle exists if the sum of two sides is greater that third side.

Apply this theorem on each combination.

Case I:

     ...(1)

Case II:

    ...(2)

Case III:

    ...(3)

On combining (1), (2) and (3), we get

Therefore, the correct option is A.