Solve 9/2=3/4(z+2/3)

$$\frac { 9 } { 2 } = \frac { 3 } { 4 } ( z + \frac { 2 } { 3 } )$$

Solve for z

$$z = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

Steps for Solving Linear Equation

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$\frac{9}{2}\times \frac{4}{3}=z+\frac{2}{3}$$

Multiply \frac{9}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 4}{2\times 3}=z+\frac{2}{3}$$

Do the multiplications in the fraction \frac{9\times 4}{2\times 3}.

$$\frac{36}{6}=z+\frac{2}{3}$$

Divide 36 by 6 to get 6.

$$6=z+\frac{2}{3}$$

Swap sides so that all variable terms are on the left hand side.

$$z+\frac{2}{3}=6$$

Subtract \frac{2}{3} from both sides.

$$z=6-\frac{2}{3}$$

Convert 6 to fraction \frac{18}{3}.

$$z=\frac{18}{3}-\frac{2}{3}$$

Since \frac{18}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$z=\frac{18-2}{3}$$

Subtract 2 from 18 to get 16.

$$z=\frac{16}{3}$$