If AG = 7x+9 and GB = 12x - 6, find the length of AB

(1 point)
AB=

1 answer

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 \( 19x + 3 \).