Answer:
Step-by-step explanation:
- Triangle inequality:
- for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side
Apply to the given triangle:
- 2x + 1 + x + 16 > 2x+ 31 ⇒ 3x - 2x > 31 - 17 ⇒ x > 14
- 2x + 1 + 2x + 31 > x + 16 ⇒ 4x - x > 16 - 32 ⇒ 3x > -16 ⇒ x > -16/3
- 2x + 31 + x + 16 > 2x + 1 ⇒ 3x - 2x > 1 - 47 ⇒ x > - 46
Combination of the three inequalities:
