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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 < .
