Simplify the following expression. \( \left(-\frac{8}{5} z-\frac{1}{2}\right)+\left(5 z-\frac{5}{4}\right) \)

To simplify the expression \( \left(-\frac{8}{5} z - \frac{1}{2}\right) + \left(5 z - \frac{5}{4}\right) \), we first combine the like terms for \( z \) and the constant terms. 1. For the \( z \) terms: \[ -\frac{8}{5} z + 5 z = -\frac{8}{5} z + \frac{25}{5} z = \frac{17}{5} z \] 2. For the constant terms: \[ -\frac{1}{2} - \frac{5}{4} \] We need a common denominator to combine these fractions. The common denominator of 2 and 4 is 4. So, we convert \(-\frac{1}{2}\) to \(-\frac{2}{4}\): \[ -\frac{2}{4} - \frac{5}{4} = -\frac{7}{4} \] Now combining both results, we have: \[ \frac{17}{5} z - \frac{7}{4} \] Thus, the simplified expression is: \[ \frac{17}{5} z - \frac{7}{4} \]