The lengths of two sides of a triangle are 7cm and 10cm. what are the upper and lower bounds on the third side of the triangle?

The lengths of two side of a triangle must add to more than the third side.

So the third side x must be less than 10 + 7 which is 17. The third side must add to 7 to be more than 10 also. So x > 3.

The final expression you get is:

3 < x < 17