#### Answer

10.5

#### Work Step by Step

In order to solve the equation, we must first get the terms with variables all on one side of the equation and the constant numbers on the other side of the equation. Then, we must isolate the variable. Note, to check the solution, we plug the found value back into the equation and check that both sides of the equation get the same value. Also, it is sometimes beneficial to multiply both sides of the equation by a constant to eliminate the fractions. Doing this, we obtain:
$$ 12z + 14z = 273 \\ z= 10.5$$
Checking:
$$ \frac{4}{7}(10.5) +\frac{2}{3}(10.5) = 13 \\ 13=13$$