Final answer:
To find AB, substitute the given values into the equation AB + CB = AC and solve for x. Then substitute the value of x back into AB to find its length.
Step-by-step explanation:
To find AB, we can use the fact that AB + CB = AC. We know that AC = 19, CB = 21 + 4x, and AB = -14 - 7x. So, we can substitute these values into the equation to solve for x.
AB + CB = AC
-14 - 7x + 21 + 4x = 19
-14 - 7x + 21 + 4x - 19 = 0
-3x - 14 + 21 - 19 = 0
-3x - 12 = 0
-3x = 12
x = -4
Now that we have the value of x, we can substitute it back into either AB or CB to find the length of the segment. Let's substitute it into AB:
AB = -14 - 7(-4)
AB = -14 + 28
AB = 14