Solve 2(2/3y+4/3)-3y=6

$$2 ( \frac { 2 } { 3 } y + \frac { 4 } { 3 } ) - 3 y = 6$$

Solve for y

$$y=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \frac{2}{3}y+\frac{4}{3}.

$$2\times \frac{2}{3}y+2\times \frac{4}{3}-3y=6$$

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

$$\frac{2\times 2}{3}y+2\times \frac{4}{3}-3y=6$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3}y+2\times \frac{4}{3}-3y=6$$

Express 2\times \frac{4}{3} as a single fraction.

$$\frac{4}{3}y+\frac{2\times 4}{3}-3y=6$$

Multiply 2 and 4 to get 8.

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

Combine \frac{4}{3}y and -3y to get -\frac{5}{3}y.

$$-\frac{5}{3}y+\frac{8}{3}=6$$

Subtract \frac{8}{3} from both sides.

$$-\frac{5}{3}y=6-\frac{8}{3}$$

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

$$-\frac{5}{3}y=\frac{18}{3}-\frac{8}{3}$$

Since \frac{18}{3} and \frac{8}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{3}y=\frac{18-8}{3}$$

Subtract 8 from 18 to get 10.

$$-\frac{5}{3}y=\frac{10}{3}$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}.

$$y=\frac{10}{3}\left(-\frac{3}{5}\right)$$

Multiply \frac{10}{3} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{10\left(-3\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{10\left(-3\right)}{3\times 5}.

$$y=\frac{-30}{15}$$

Divide -30 by 15 to get -2.

$$y=-2$$