Solve 2/5(1/2y+5)-4/5=1/2y-1+frac{1}{10}y

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

Solve for y

$$y = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

Steps for Solving Linear Equation

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

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

Multiply \frac{2}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Cancel out 5 and 5.

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

Convert 2 to fraction \frac{10}{5}.

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

Since \frac{10}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 10 to get 6.

$$\frac{1}{5}y+\frac{6}{5}=\frac{1}{2}y-1+\frac{1}{10}y$$

Combine \frac{1}{2}y and \frac{1}{10}y to get \frac{3}{5}y.

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

Subtract \frac{3}{5}y from both sides.

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

Combine \frac{1}{5}y and -\frac{3}{5}y to get -\frac{2}{5}y.

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

Subtract \frac{6}{5} from both sides.

$$-\frac{2}{5}y=-1-\frac{6}{5}$$

Convert -1 to fraction -\frac{5}{5}.

$$-\frac{2}{5}y=-\frac{5}{5}-\frac{6}{5}$$

Since -\frac{5}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{5}y=\frac{-5-6}{5}$$

Subtract 6 from -5 to get -11.

$$-\frac{2}{5}y=-\frac{11}{5}$$

Multiply both sides by -\frac{5}{2}, the reciprocal of -\frac{2}{5}.

$$y=-\frac{11}{5}\left(-\frac{5}{2}\right)$$

Multiply -\frac{11}{5} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-11\left(-5\right)}{5\times 2}$$

Do the multiplications in the fraction \frac{-11\left(-5\right)}{5\times 2}.

$$y=\frac{55}{10}$$

Reduce the fraction \frac{55}{10} to lowest terms by extracting and canceling out 5.

$$y=\frac{11}{2}$$