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

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

Solve for y

$$y=-2$$

Steps for Solving Linear Equation

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

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

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

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

Combine \frac{2}{3}y and \frac{1}{2}y to get \frac{7}{6}y.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}\left(1-2y\right)-4$$

Use the distributive property to multiply \frac{2}{5} by 1-2y.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{2}{5}\left(-2\right)y-4$$

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

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{2\left(-2\right)}{5}y-4$$

Multiply 2 and -2 to get -4.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{-4}{5}y-4$$

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}-\frac{4}{5}y-4$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}-\frac{4}{5}y-\frac{20}{5}$$

Since \frac{2}{5} and \frac{20}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2-20}{5}-\frac{4}{5}y$$

Subtract 20 from 2 to get -18.

$$\frac{7}{6}y+\frac{1}{3}=-\frac{18}{5}-\frac{4}{5}y$$

Add \frac{4}{5}y to both sides.

$$\frac{7}{6}y+\frac{1}{3}+\frac{4}{5}y=-\frac{18}{5}$$

Combine \frac{7}{6}y and \frac{4}{5}y to get \frac{59}{30}y.

$$\frac{59}{30}y+\frac{1}{3}=-\frac{18}{5}$$

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

$$\frac{59}{30}y=-\frac{18}{5}-\frac{1}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{18}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{59}{30}y=-\frac{54}{15}-\frac{5}{15}$$

Since -\frac{54}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59}{30}y=\frac{-54-5}{15}$$

Subtract 5 from -54 to get -59.

$$\frac{59}{30}y=-\frac{59}{15}$$

Multiply both sides by \frac{30}{59}, the reciprocal of \frac{59}{30}.

$$y=-\frac{59}{15}\times \frac{30}{59}$$

Multiply -\frac{59}{15} times \frac{30}{59} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-59\times 30}{15\times 59}$$

Do the multiplications in the fraction \frac{-59\times 30}{15\times 59}.

$$y=\frac{-1770}{885}$$

Divide -1770 by 885 to get -2.

$$y=-2$$