Question

A triangle has sides x,x+7 , x+ 8. The value of x must fall between what boundaries to make this an obtuse triangle?

Answer 1

any side of a triangle is less than the sum of the other two sides.

x < x+7 + x+8
-15 < x
no problem there

x+7 < x + x+8
-1 < x
no problem there

x+8 < x + x+7
1 < x

so, as long as x is at least 1, the three values could form a triangle.