To find the length of segment \( AB \), we need to add the lengths of segments \( AM \) and \( MB \).
Given:
- \( AM = 3x + 8 \)
- \( MB = 6x - 4 \)
We can express \( AB \) as follows: \[ AB = AM + MB \] Substituting the given expressions for \( AM \) and \( MB \): \[ AB = (3x + 8) + (6x - 4) \]
Now, combine like terms: \[ AB = 3x + 6x + 8 - 4 \] \[ AB = 9x + 4 \]
Thus, the expression for the length of \( AB \) is: \[ AB = 9x + 4 \]
If you need a specific value for \( AB \), you'll need to provide a value for \( x \). Otherwise, the expression above is the final answer for the length of segment \( AB \).