Answer:
2 ≤ x ≤ 7
Step-by-step explanation:
Due to the triangle inequality, the sum of two sides of a triangle must be greater than or equal to the remaining side.
Therefore,
5+7 ≥ 2x-2
=> 12 ≥ 2x-2
=> 14 ≥ 2x
=> 7 ≥ x
However, notice that BC + AB must be ≥ 7, So,
5 + 2x - 2 ≥ 7
=> 2x - 2 ≥ 2
=> 2x ≥ 4
=> x ≥ 2
Therefore, both bound of x have been found.
