Answer:
Explanation:
To determine the length of AB, we need to find the value of x.
We are given that AC = 2x + 7, BC = x, and AB = 5x + 9.
Since B is on the line segment AC, the sum of lengths AB and BC should equal the length of AC. Therefore, we can set up the equation:
AB + BC = AC
Substituting the given values, we have:
(5x + 9) + x = 2x + 7
Simplifying the equation:
6x + 9 = 2x + 7
Bringing like terms to one side:
6x - 2x = 7 - 9
4x = -2
Dividing both sides by 4:
x = -2/4
Simplifying:
x = -1/2
Now that we have the value of x, we can substitute it back into the expression for AB to find its numerical length:
AB = 5x + 9 = 5(-1/2) + 9 = -5/2 + 9 = (18 - 5)/2 = 13/2 = 6.5
Therefore, the numerical length of AB is 6.5.