Final answer:
To find the value of AB, we use the equation AC = AB + BC. Solving for x and substituting the value back into the equation gives us AB = 5.
Step-by-step explanation:
We are given that B is between A and C. Let's find the value of AB using the information given.
Since B is between A and C, we can write:
AC = AB + BC
Substituting the given values:
5x-7 = x+2 + 2x-3
Combine like terms and solve for x:
5x-7 = 3x-1
2x = 6
x = 3
Now, substitute the value of x back into one of the equations to find AB:
AB = x+2 = 3+2 = 5
Therefore, AB = 5.