Solve y=y/4+5/2

$$y= \frac{ y }{ 4 } + \frac{ 5 }{ 2 }$$

Solve for y

$$y = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{5}{2} times \frac{2}{2}.

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

Since \frac{y}{4} and \frac{5\times 2}{4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in y+5\times 2.

$$y=\frac{y+10}{4}$$

Divide each term of y+10 by 4 to get \frac{1}{4}y+\frac{5}{2}.

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

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

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

Combine y and -\frac{1}{4}y to get \frac{3}{4}y.

$$\frac{3}{4}y=\frac{5}{2}$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$y=\frac{5}{2}\times \frac{4}{3}$$

Multiply \frac{5}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{5\times 4}{2\times 3}$$

Do the multiplications in the fraction \frac{5\times 4}{2\times 3}.

$$y=\frac{20}{6}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$y=\frac{10}{3}$$