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}.

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

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

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

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{13}{3}y.

$$-\frac{13}{3}y+\frac{8}{3}=-6$$

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

$$-\frac{13}{3}y=-6-\frac{8}{3}$$

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

$$-\frac{13}{3}y=-\frac{18}{3}-\frac{8}{3}$$

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

$$-\frac{13}{3}y=\frac{-18-8}{3}$$

Subtract 8 from -18 to get -26.

$$-\frac{13}{3}y=-\frac{26}{3}$$

Multiply both sides by -\frac{3}{13}, the reciprocal of -\frac{13}{3}.

$$y=-\frac{26}{3}\left(-\frac{3}{13}\right)$$

Multiply -\frac{26}{3} times -\frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-26\left(-3\right)}{3\times 13}$$

Do the multiplications in the fraction \frac{-26\left(-3\right)}{3\times 13}.

$$y=\frac{78}{39}$$

Divide 78 by 39 to get 2.

$$y=2$$