Answer:
9 (see below)
Step-by-step explanation:
So, for a triangle, if you add any two sides, it will always be greater than the third side.
So if a triangle has sides of 1, 1, and 1:
1 + 1 > 1
1 + 1 > 1
1 + 1 > 1
So this is a triangle.
For a triangle with the sides of 3, 3, and 9:
3 + 9 > 3
9 + 3 > 3
3 + 3 > 9 (this one is not true)
So, these can't be the values of the sides of a triangle.
For your situation, you have a triangle with sides of 4, 6, and x.
We need to find out what x is, so:
4 + 6 > x
4 + x > 6
6 + x > 4
Isolate x to one side and simplify all the inequalities. You will get:
x < 10
x > 2
x > -2
So, -2 < x < 10.
If you plug in your answer choices, it will be 9.
