Solve 5(y+2/3)-3=4(3y-1/2)

$$5(y+ \frac{ 2 }{ 3 } )-3=4(3y- \frac{ 1 }{ 2 } )$$

Solve for y

$$y=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

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

$$5y+5\times \frac{2}{3}-3=4\left(3y-\frac{1}{2}\right)$$

Express 5\times \frac{2}{3} as a single fraction.

$$5y+\frac{5\times 2}{3}-3=4\left(3y-\frac{1}{2}\right)$$

Multiply 5 and 2 to get 10.

$$5y+\frac{10}{3}-3=4\left(3y-\frac{1}{2}\right)$$

Convert 3 to fraction \frac{9}{3}.

$$5y+\frac{10}{3}-\frac{9}{3}=4\left(3y-\frac{1}{2}\right)$$

Since \frac{10}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$5y+\frac{10-9}{3}=4\left(3y-\frac{1}{2}\right)$$

Subtract 9 from 10 to get 1.

$$5y+\frac{1}{3}=4\left(3y-\frac{1}{2}\right)$$

Use the distributive property to multiply 4 by 3y-\frac{1}{2}.

$$5y+\frac{1}{3}=12y+4\left(-\frac{1}{2}\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$5y+\frac{1}{3}=12y+\frac{4\left(-1\right)}{2}$$

Multiply 4 and -1 to get -4.

$$5y+\frac{1}{3}=12y+\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$5y+\frac{1}{3}=12y-2$$

Subtract 12y from both sides.

$$5y+\frac{1}{3}-12y=-2$$

Combine 5y and -12y to get -7y.

$$-7y+\frac{1}{3}=-2$$

Subtract \frac{1}{3} from both sides.

$$-7y=-2-\frac{1}{3}$$

Convert -2 to fraction -\frac{6}{3}.

$$-7y=-\frac{6}{3}-\frac{1}{3}$$

Since -\frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$-7y=\frac{-6-1}{3}$$

Subtract 1 from -6 to get -7.

$$-7y=-\frac{7}{3}$$

Divide both sides by -7.

$$y=\frac{-\frac{7}{3}}{-7}$$

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

$$y=\frac{-7}{3\left(-7\right)}$$

Cancel out -7 in both numerator and denominator.

$$y=\frac{1}{3}$$