Final answer:
To find the length of AB, you need to solve the equation AB=x+2 and use the fact that the sum of the lengths of two sides of a triangle is greater than the length of the third side.
Step-by-step explanation:
To find the length of AB, we need to solve the equation AB=x+2. Given that B is between A and C, we can use the fact that the sum of the lengths of two sides of a triangle is greater than the length of the third side.
Therefore, we have the following inequality: AB + BC > AC.
Substituting the given expressions, we get (x+2) + (2x-3) > 5x-7.
Solving this inequality, we find that x > 3.
Then, substituting x=3 into
AB=x+2,
we get AB = 3+2
= 5.