Solve 1/8(3y+2)=1/4(2y+1/2)+1/2

$$\frac { 1 } { 8 } ( 3 y + 2 ) = \frac { 1 } { 4 } ( 2 y + \frac { 1 } { 2 } ) + \frac { 1 } { 2 }$$

Solve for y

$$y=-3$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{8} by 3y+2.

$$\frac{1}{8}\times 3y+\frac{1}{8}\times 2=\frac{1}{4}\left(2y+\frac{1}{2}\right)+\frac{1}{2}$$

Multiply \frac{1}{8} and 3 to get \frac{3}{8}.

$$\frac{3}{8}y+\frac{1}{8}\times 2=\frac{1}{4}\left(2y+\frac{1}{2}\right)+\frac{1}{2}$$

Multiply \frac{1}{8} and 2 to get \frac{2}{8}.

$$\frac{3}{8}y+\frac{2}{8}=\frac{1}{4}\left(2y+\frac{1}{2}\right)+\frac{1}{2}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{8}y+\frac{1}{4}=\frac{1}{4}\left(2y+\frac{1}{2}\right)+\frac{1}{2}$$

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

$$\frac{3}{8}y+\frac{1}{4}=\frac{1}{4}\times 2y+\frac{1}{4}\times \frac{1}{2}+\frac{1}{2}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{3}{8}y+\frac{1}{4}=\frac{2}{4}y+\frac{1}{4}\times \frac{1}{2}+\frac{1}{2}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{8}y+\frac{1}{4}=\frac{1}{2}y+\frac{1}{4}\times \frac{1}{2}+\frac{1}{2}$$

Multiply \frac{1}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{8}y+\frac{1}{4}=\frac{1}{2}y+\frac{1\times 1}{4\times 2}+\frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 2}.

$$\frac{3}{8}y+\frac{1}{4}=\frac{1}{2}y+\frac{1}{8}+\frac{1}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{1}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{3}{8}y+\frac{1}{4}=\frac{1}{2}y+\frac{1}{8}+\frac{4}{8}$$

Since \frac{1}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{3}{8}y+\frac{1}{4}=\frac{1}{2}y+\frac{1+4}{8}$$

Add 1 and 4 to get 5.

$$\frac{3}{8}y+\frac{1}{4}=\frac{1}{2}y+\frac{5}{8}$$

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

$$\frac{3}{8}y+\frac{1}{4}-\frac{1}{2}y=\frac{5}{8}$$

Combine \frac{3}{8}y and -\frac{1}{2}y to get -\frac{1}{8}y.

$$-\frac{1}{8}y+\frac{1}{4}=\frac{5}{8}$$

Subtract \frac{1}{4} from both sides.

$$-\frac{1}{8}y=\frac{5}{8}-\frac{1}{4}$$

Least common multiple of 8 and 4 is 8. Convert \frac{5}{8} and \frac{1}{4} to fractions with denominator 8.

$$-\frac{1}{8}y=\frac{5}{8}-\frac{2}{8}$$

Since \frac{5}{8} and \frac{2}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{8}y=\frac{5-2}{8}$$

Subtract 2 from 5 to get 3.

$$-\frac{1}{8}y=\frac{3}{8}$$

Multiply both sides by -8, the reciprocal of -\frac{1}{8}.

$$y=\frac{3}{8}\left(-8\right)$$

Express \frac{3}{8}\left(-8\right) as a single fraction.

$$y=\frac{3\left(-8\right)}{8}$$

Multiply 3 and -8 to get -24.

$$y=\frac{-24}{8}$$

Divide -24 by 8 to get -3.

$$y=-3$$