To solve the equation \( 9z + 9z - 2 = 12 \), we can first simplify the left side:
\[ 9z + 9z - 2 = 12z - 2 \]
So the equation now is:
\[ 12z - 2 = 12 \]
Next, we add 2 to both sides to isolate the term with \( z \):
\[ 12z = 12 + 2 \]
\[ 12z = 14 \]
Now, we divide both sides by 12 to solve for \( z \):
\[ z = \frac{14}{12} = \frac{7}{6} \]
Thus, the solution to the equation \( 9z + 9z - 2 = 12 \) is:
\[ z = \frac{7}{6} \]
Since this value does not match any of the listed response options (which seem incorrectly formatted), it appears none of the options provided (12, \( \frac{1}{2} \), 12 and \( \frac{3}{2} \), 3, no solution) correspond accurately to \( z = \frac{7}{6} \).
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