Restriction on x for a triangle

Question

Triangle ABC: length of side AB is 3x+1, length of side AC is 4x-2, length of side BC is 5x+7. Find the restrictions on x

Answer 1

In a triangle, a length of each side is less than the sum of lengths of two other sides.

Therefore,

3x +1 < 4x - 2 + 5x + 7 --> x > - 2/3

4x - 2 < 3x + 1 + 5x + 7 --> x > - 2.5

5x + 7 < 3x + 1 + 4x - 2 --> x > 4

Answer: x > 4