Two sides of a triangle are lengths of 7 and 15 units. Write an inequality for the possible lengths of the third side x

8 < x < 22

Step-by-step explanation:

The triangle inequality theorem tells us that if two sides of a triangle are known, the side length of the 3rd side would be in between the sum and difference of the side lengths of the other two sides.

If the 2 known sides of a triangle are "a" and "b", and the unknown side is "x", we can say that (given a > b):

a - b < x < a + b

In this problem, the 2 known sides are 7 and 15 units, the third side is "x", so:

Sum = 7 + 15 = 22

Difference = 15 - 7 = 8

Thus,

Difference < x < Sum

8 < x < 22