Solve z=-16-7-(5-z/3)/9

$$z = \frac{ -16-7-( \frac{ 5-z }{ 3 } ) }{ 9 }$$

Solve for z

$$z = -\frac{37}{13} = -2\frac{11}{13} \approx -2.846153846$$

Steps for Solving Linear Equation

Subtract 7 from -16 to get -23.

$$z=\frac{-23-\frac{5-z}{3}}{9}$$

Divide each term of 5-z by 3 to get \frac{5}{3}-\frac{1}{3}z.

$$z=\frac{-23-\left(\frac{5}{3}-\frac{1}{3}z\right)}{9}$$

To find the opposite of \frac{5}{3}-\frac{1}{3}z, find the opposite of each term.

$$z=\frac{-23-\frac{5}{3}-\left(-\frac{1}{3}z\right)}{9}$$

The opposite of -\frac{1}{3}z is \frac{1}{3}z.

$$z=\frac{-23-\frac{5}{3}+\frac{1}{3}z}{9}$$

Convert -23 to fraction -\frac{69}{3}.

$$z=\frac{-\frac{69}{3}-\frac{5}{3}+\frac{1}{3}z}{9}$$

Since -\frac{69}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$z=\frac{\frac{-69-5}{3}+\frac{1}{3}z}{9}$$

Subtract 5 from -69 to get -74.

$$z=\frac{-\frac{74}{3}+\frac{1}{3}z}{9}$$

Divide each term of -\frac{74}{3}+\frac{1}{3}z by 9 to get -\frac{74}{27}+\frac{1}{27}z.

$$z=-\frac{74}{27}+\frac{1}{27}z$$

Subtract \frac{1}{27}z from both sides.

$$z-\frac{1}{27}z=-\frac{74}{27}$$

Combine z and -\frac{1}{27}z to get \frac{26}{27}z.

$$\frac{26}{27}z=-\frac{74}{27}$$

Multiply both sides by \frac{27}{26}, the reciprocal of \frac{26}{27}.

$$z=-\frac{74}{27}\times \frac{27}{26}$$

Multiply -\frac{74}{27} times \frac{27}{26} by multiplying numerator times numerator and denominator times denominator.

$$z=\frac{-74\times 27}{27\times 26}$$

Cancel out 27 in both numerator and denominator.

$$z=\frac{-74}{26}$$

Reduce the fraction \frac{-74}{26} to lowest terms by extracting and canceling out 2.

$$z=-\frac{37}{13}$$