Solve 4y-5/2-2y-1/6=y

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

Solve for y

$$y = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 6 is 6. Multiply \frac{4y-5}{2} times \frac{3}{3}.

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

Since \frac{3\left(4y-5\right)}{6} and \frac{2y-1}{6} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\left(4y-5\right)-\left(2y-1\right).

$$\frac{12y-15-2y+1}{6}=y$$

Combine like terms in 12y-15-2y+1.

$$\frac{10y-14}{6}=y$$

Divide each term of 10y-14 by 6 to get \frac{5}{3}y-\frac{7}{3}.

$$\frac{5}{3}y-\frac{7}{3}=y$$

Subtract y from both sides.

$$\frac{5}{3}y-\frac{7}{3}-y=0$$

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

$$\frac{2}{3}y-\frac{7}{3}=0$$

Add \frac{7}{3} to both sides. Anything plus zero gives itself.

$$\frac{2}{3}y=\frac{7}{3}$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$y=\frac{7}{3}\times \frac{3}{2}$$

Multiply \frac{7}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{7\times 3}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$y=\frac{7}{2}$$