1. The problem is to add the fractions $\frac{12}{7}$ and $-\frac{5}{7}$.\n\n2. Since the denominators are the same, we can add the numerators directly: $$\frac{12}{7} + \left(-\frac{5}{7}\right) = \frac{12 + (-5)}{7}$$\n\n3. Simplify the numerator: $$\frac{12 - 5}{7} = \frac{7}{7}$$\n\n4. Simplify the fraction by canceling the common factor 7: $$\frac{\cancel{7}}{\cancel{7}} = 1$$\n\n5. Therefore, the sum is $1$.\n\nYes, if you got $z = 1$, you are correct.