Find the range of $x$ if $6, 8, x$ make the sides of triangle.

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Solution

According to triangle inequality,
The sum of 2 sides is more than third side
$⟹ x < 6 + 8 x < 14$
The difference of 2 sides is less than third side
$⟹ x > 8 - 6 x > 2 x \in (2, 14)$

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