Final answer:
To find the value of AC in terms of x, we add the given expressions for AB and BC and solve for x. After finding x, we substitute it back into the expression for AC to get the exact length, which is 48.
Step-by-step explanation:
The question involves finding the value of AC in terms of x from the information given about segment lengths AB, BC, and AC in a line. Assuming that point A, B, and C are positioned on a line segment in that order, the length of AC is the sum of AB and BC. Therefore, we can set up the equation:
AC = AB + BC
Substituting the given expressions, we get:
9x - 15 = (4x + 10) + (2x - 4)
Simplifying this equation:
9x - 15 = 4x + 10 + 2x - 4
9x - 15 = 6x + 6
Combining like terms, we subtract 6x from both sides:
3x - 15 = 6
Adding 15 to both sides to isolate the x term:
3x = 21
Dividing both sides by 3, we find:
x = 7
Now, we can substitute x = 7 back into the expression for AC:
AC = 9x - 15
AC = 9(7) - 15
AC = 63 - 15
AC = 48
Finally, the exact value of AC is 48.