## Intermediate Algebra: Connecting Concepts through Application

$z=\frac{17}{6}$
$\frac{3}{7}(2z-5)=\frac{4}{7}(-3z+9)$ $\frac{6}{7}z-\frac{15}{7}=-\frac{12}{7}z+\frac{36}{7}$ $\frac{6}{7}z+\frac{12}{7}z=\frac{36}{7}+\frac{15}{7}$ $\frac{18}{7}z=\frac{51}{7}$ $z=\frac{51}{7}\times\frac{7}{18}$ $z=\frac{51}{18}$ (to simplify, divide both numbers by 3) $z=\frac{17}{6}$