To find the length of \( AB \), we can start by adding the lengths of \( AG \) and \( GB \):
\[ AB = AG + GB \]
Given: \[ AG = 7x + 9 \] \[ GB = 12x - 6 \]
Now, substituting the expressions for \( AG \) and \( GB \) into the equation for \( AB \):
\[ AB = (7x + 9) + (12x - 6) \]
Combining like terms:
\[ AB = 7x + 12x + 9 - 6 \] \[ AB = 19x + 3 \]
So, the expression for the length of \( AB \) in terms of \( x \) is:
\[ AB = 19x + 3 \]
If you have a specific value for \( x \), you can substitute it into the equation to find the numeric length of \( AB \). If no value for \( x \) is provided, \( AB \) remains as \( 19x + 3 \).