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