Solve 1/3(4z+8)-16=-2/3(9z-12)

$$\frac { 1 } { 3 } ( 4 z + 8 ) - 16 = - \frac { 2 } { 3 } ( 9 z - 12 )$$

Solve for z

$$z = \frac{32}{11} = 2\frac{10}{11} \approx 2.909090909$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 4z+8.

$$\frac{1}{3}\times 4z+\frac{1}{3}\times 8-16=-\frac{2}{3}\left(9z-12\right)$$

Multiply \frac{1}{3} and 4 to get \frac{4}{3}.

$$\frac{4}{3}z+\frac{1}{3}\times 8-16=-\frac{2}{3}\left(9z-12\right)$$

Multiply \frac{1}{3} and 8 to get \frac{8}{3}.

$$\frac{4}{3}z+\frac{8}{3}-16=-\frac{2}{3}\left(9z-12\right)$$

Convert 16 to fraction \frac{48}{3}.

$$\frac{4}{3}z+\frac{8}{3}-\frac{48}{3}=-\frac{2}{3}\left(9z-12\right)$$

Since \frac{8}{3} and \frac{48}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}z+\frac{8-48}{3}=-\frac{2}{3}\left(9z-12\right)$$

Subtract 48 from 8 to get -40.

$$\frac{4}{3}z-\frac{40}{3}=-\frac{2}{3}\left(9z-12\right)$$

Use the distributive property to multiply -\frac{2}{3} by 9z-12.

$$\frac{4}{3}z-\frac{40}{3}=-\frac{2}{3}\times 9z-\frac{2}{3}\left(-12\right)$$

Express -\frac{2}{3}\times 9 as a single fraction.

$$\frac{4}{3}z-\frac{40}{3}=\frac{-2\times 9}{3}z-\frac{2}{3}\left(-12\right)$$

Multiply -2 and 9 to get -18.

$$\frac{4}{3}z-\frac{40}{3}=\frac{-18}{3}z-\frac{2}{3}\left(-12\right)$$

Divide -18 by 3 to get -6.

$$\frac{4}{3}z-\frac{40}{3}=-6z-\frac{2}{3}\left(-12\right)$$

Express -\frac{2}{3}\left(-12\right) as a single fraction.

$$\frac{4}{3}z-\frac{40}{3}=-6z+\frac{-2\left(-12\right)}{3}$$

Multiply -2 and -12 to get 24.

$$\frac{4}{3}z-\frac{40}{3}=-6z+\frac{24}{3}$$

Divide 24 by 3 to get 8.

$$\frac{4}{3}z-\frac{40}{3}=-6z+8$$

Add 6z to both sides.

$$\frac{4}{3}z-\frac{40}{3}+6z=8$$

Combine \frac{4}{3}z and 6z to get \frac{22}{3}z.

$$\frac{22}{3}z-\frac{40}{3}=8$$

Add \frac{40}{3} to both sides.

$$\frac{22}{3}z=8+\frac{40}{3}$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{22}{3}z=\frac{24}{3}+\frac{40}{3}$$

Since \frac{24}{3} and \frac{40}{3} have the same denominator, add them by adding their numerators.

$$\frac{22}{3}z=\frac{24+40}{3}$$

Add 24 and 40 to get 64.

$$\frac{22}{3}z=\frac{64}{3}$$

Multiply both sides by \frac{3}{22}, the reciprocal of \frac{22}{3}.

$$z=\frac{64}{3}\times \frac{3}{22}$$

Multiply \frac{64}{3} times \frac{3}{22} by multiplying numerator times numerator and denominator times denominator.

$$z=\frac{64\times 3}{3\times 22}$$

Cancel out 3 in both numerator and denominator.

$$z=\frac{64}{22}$$

Reduce the fraction \frac{64}{22} to lowest terms by extracting and canceling out 2.

$$z=\frac{32}{11}$$