Hi, i have a question on the restrictions of this triangle. The side lengths for a triangle are 2x+3, 3x-5 an x+5. The triangle is scalene. I've included a picture below. The restrictions on a triangle can't be as simple as solving for x for each side can it? The question asks: For what values of x is the triangle possible?
any two sides of a triangle must sum to be greater than the third side ...
(2x+3) + (3x-5) > x+5
(2x+3) + (x+5) > 3x-5
(3x-5) + (x+5) > 2x+3
solve all three inequalities and find the intersection of their solution sets to determine all possible values for x.