Find all possible values of x if these represent side of a triangle 2x,5-x,4

-1/3 < x < 3 or x = (-1/3, 3)

Step-by-step explanation:

Given sides of a triangle:

2x, 5 - x, 4

Triangle inequality theorem:

Any side is smaller than the some of the other two.

Apply to the given triangle:

2x + 5 - x > 4 ⇒ x > -12x + 4 > 5 - x ⇒ 3x > -1 ⇒ x > -1/35 - x + 4 > 2x ⇒ 3x < 9 ⇒ x < 3

Combine all the inequalities:

-1/3 < x < 3x = (-1/3, 3)

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