Answer:
- -1/3 < x < 3 or x = (-1/3, 3)
Step-by-step explanation:
Given sides of a triangle:
Triangle inequality theorem:
- Any side is smaller than the some of the other two.
Apply to the given triangle:
- 2x + 5 - x > 4 ⇒ x > -1
- 2x + 4 > 5 - x ⇒ 3x > -1 ⇒ x > -1/3
- 5 - x + 4 > 2x ⇒ 3x < 9 ⇒ x < 3
Combine all the inequalities:
- -1/3 < x < 3
- x = (-1/3, 3)
