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

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

Solve for y

$$y=23$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{5} by 2y+4.

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

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

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

Multiply \frac{1}{5} and 4 to get \frac{4}{5}.

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

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

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

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

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Subtract \frac{1}{2}y from both sides.

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

Combine \frac{2}{5}y and -\frac{1}{2}y to get -\frac{1}{10}y.

$$-\frac{1}{10}y+\frac{4}{5}=-\frac{3}{2}$$

Subtract \frac{4}{5} from both sides.

$$-\frac{1}{10}y=-\frac{3}{2}-\frac{4}{5}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{3}{2} and \frac{4}{5} to fractions with denominator 10.

$$-\frac{1}{10}y=-\frac{15}{10}-\frac{8}{10}$$

Since -\frac{15}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{10}y=\frac{-15-8}{10}$$

Subtract 8 from -15 to get -23.

$$-\frac{1}{10}y=-\frac{23}{10}$$

Multiply both sides by -10, the reciprocal of -\frac{1}{10}.

$$y=-\frac{23}{10}\left(-10\right)$$

Express -\frac{23}{10}\left(-10\right) as a single fraction.

$$y=\frac{-23\left(-10\right)}{10}$$

Multiply -23 and -10 to get 230.

$$y=\frac{230}{10}$$

Divide 230 by 10 to get 23.

$$y=23$$