Solve 2(7/3-5/3y)+7y=12

$$2 ( \frac { 7 } { 3 } - \frac { 5 } { 3 } y ) + 7 y = 12$$

Solve for y

$$y=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \frac{7}{3}-\frac{5}{3}y.

$$2\times \frac{7}{3}+2\left(-\frac{5}{3}\right)y+7y=12$$

Express 2\times \frac{7}{3} as a single fraction.

$$\frac{2\times 7}{3}+2\left(-\frac{5}{3}\right)y+7y=12$$

Multiply 2 and 7 to get 14.

$$\frac{14}{3}+2\left(-\frac{5}{3}\right)y+7y=12$$

Express 2\left(-\frac{5}{3}\right) as a single fraction.

$$\frac{14}{3}+\frac{2\left(-5\right)}{3}y+7y=12$$

Multiply 2 and -5 to get -10.

$$\frac{14}{3}+\frac{-10}{3}y+7y=12$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{14}{3}-\frac{10}{3}y+7y=12$$

Combine -\frac{10}{3}y and 7y to get \frac{11}{3}y.

$$\frac{14}{3}+\frac{11}{3}y=12$$

Subtract \frac{14}{3} from both sides.

$$\frac{11}{3}y=12-\frac{14}{3}$$

Convert 12 to fraction \frac{36}{3}.

$$\frac{11}{3}y=\frac{36}{3}-\frac{14}{3}$$

Since \frac{36}{3} and \frac{14}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{3}y=\frac{36-14}{3}$$

Subtract 14 from 36 to get 22.

$$\frac{11}{3}y=\frac{22}{3}$$

Multiply both sides by \frac{3}{11}, the reciprocal of \frac{11}{3}.

$$y=\frac{22}{3}\times \frac{3}{11}$$

Multiply \frac{22}{3} times \frac{3}{11} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{22\times 3}{3\times 11}$$

Cancel out 3 in both numerator and denominator.

$$y=\frac{22}{11}$$

Divide 22 by 11 to get 2.

$$y=2$$