SOLUTION: A triangle has sides 45, 4x, and 2x−4. What is the possible range of x?

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Question 1024844: A triangle has sides 45, 4x, and 2x−4. What is the possible range of x?
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
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A triangle has sides 45, 4x, and 2x-4. What is the possible range of x?
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In any triangle, each side is shorter than the sum of two other sides.
It gives three independent inequality

45 < 4x + (2x-4),   (1)
4x < 45 + (2x-4),   (2)
2x-4 < 45 + 4x.     (3)

From (1),  6x > 45 + 4 = 49    --->  x > .

From (2),  2x < 45 - 4 = 41    --->  x < .

From (3),  2x > -4 - 45 = -49  --->  x > .

Answer.  < x < .


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