A triangle has side lengths of 1, 1 - c, and 1 - 2c. What are all the possible values of c?
So a triangle's legs' sum must exceed the hypothenuse to be a triangle.
First, assuming c is positive, we have 1-2c and 1-c as the legs as they are each smaller than 1.
1-2c + 1-c >1
c < 1/3
That's after a bit of rearrangement.
NOW assuming c is 0. Hmm. That doesn't work since 1+1 = 2. Hmm.
NOW assuming that c is negative.
1-2c must be the hypothenuse as it is the largest, and 1 and 1-c are the legs.
1 + 1-c > 1-2c
2-c > 1-2c
1 > 2c
1/2 > c
c < 1/2
since c is smaller than 1/2 AND 1/3, we go with 1/3 since it's smaller than and the smallest.
If you don't understand anythign feel free to ask.