A triangle has 2 side lengths, 3 and 8. What is the range of numbers the 3rd side could be?

5 < x < 11

Step-by-step explanation:

The third side of the triangle, x, should satisfy the following equations:

3 + 8 > x

3 + x > 8

8 + x > 3

Simplifying, we get x < 11 from the first equation. We also get 5 < x from the second equation and -5 < x. Since 5 is larger than -5, we take the more inclusive one, which is 5 < x (because 5 < x includes -5, while -5 < x doesn't include 5.)

Combining the two, we get 5 < x < 11.