What is the smallest integer x, for which x, x+5, and 2x-15 can be the lengths of the sides of a triangle?

x = 10

Step-by-step explanation:

Criterion: The sum of the shorter two sides must just barely exceed the third side.

If we assume that 2x-15 represents the third side, then write the following equation and solve it for x:

x + x+5 = 2x - 15 There is no solution to this.

If we assume that x+5 represents the third side, then x + 2x - 15 = x + 5. Attempting a solution: 3x - 15 = x + 5, or 2x = 20, or x = 10. Check: Is the sum of x and 2x-15

about equal to x+5? Is 10 + 2 (10) - 15 equal to 10 + 5? Is 30-15 = 15? Yes. x = 10

the smallest integer x can be is 11 because it has to be greater than 10