What is the range of possible sizes for side x?

Step-by-step explanation:

You use the triangle inequality theorem for this.  That theorem states that if the sides are lengths a, b, and c, then

a + b > c,

b + c > a, and

a + c > b.

Let a = 5.5, b = 3.2, and c = x.

5.5 + 3.2 > x, so 8.7 > x (aka x < 8.7)

3.2 + x > 5.5, so x > 2.3 and

5.5 + x > 3.2, so x > -2.3

Since measurements of length and distance will never be negative, our range of values for x is

2.3 < x < 8.7

If x were to be shorter than 2.3, the triangle wouldn't "close" up; likewise if one side were to be longer than 8.7...another side wouldn't "close".

step-by-step explanation: