#1**+1 **

Using the triangle inequality theorem, we can form these inequalities:

**8 + 8.8 > x**

**8 + x > 8.8**

**x + 8.8 > 8**

We technically don't need the third one, because we already know that x is greater than -0.8. (because lengthes can't be negative)

**8 + 8.8 > x**

**8 + x > 8.8**

We now need to isolate the "x" in the second inequality:

x > 8.8 - 8

**x > 0.8**

Here is what we now know about x:

x < 16.8

x > 0.8

Therefore, the range for x is: **{x | ****0.8 < x < 16.8 } **

**EXTRA KNOWLEDGE:**

This is not needed, but the range in interval notation form is **(0.8, 16.8)**

EDIT: Sorry, I used the wrong numbers!

**:)**

ilorty Aug 31, 2020