ger, simplified fraction, or decimal rounded to two decimal places. \[ \frac{7}{2} z+\frac{13}{7} z-\frac{15}{14}=\frac{5}{7} \]

First, let's combine the fractions on the left side of the equation. We start with the \( z \) terms: \[ \frac{7}{2} z + \frac{13}{7} z \] To add these fractions, we need a common denominator, which is 14. We can rewrite the fractions: \[ \frac{7}{2} z = \frac{49}{14} z \quad \text{and} \quad \frac{13}{7} z = \frac{26}{14} z \] Now we can combine them: \[ \frac{49}{14} z + \frac{26}{14} z = \frac{75}{14} z \] Now our equation looks like this: \[ \frac{75}{14} z - \frac{15}{14} = \frac{5}{7} \] Next, we can eliminate the fraction by multiplying every term by 14: \[ 75z - 15 = 10 \] Adding 15 on both sides gives us: \[ 75z = 25 \] Now, divide by 75: \[ z = \frac{25}{75} = \frac{1}{3} \] To express \( \frac{1}{3} \) as a decimal rounded to two decimal places, we get: \[ z \approx 0.33 \] In summary, the solution for \( z \) can be expressed as the fraction \( \frac{1}{3} \) or as the decimal \( 0.33 \).