Solve 2y-1/4=y-13/12+3y-5/6

$$\frac { 2 y - 1 } { 4 } = y - \frac { 13 } { 12 } + \frac { 3 y - 5 } { 6 }$$

Solve for y

$$y = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,12,6.

$$3\left(2y-1\right)=12y-13+2\left(3y-5\right)$$

Use the distributive property to multiply 3 by 2y-1.

$$6y-3=12y-13+2\left(3y-5\right)$$

Use the distributive property to multiply 2 by 3y-5.

$$6y-3=12y-13+6y-10$$

Combine 12y and 6y to get 18y.

$$6y-3=18y-13-10$$

Subtract 10 from -13 to get -23.

$$6y-3=18y-23$$

Subtract 18y from both sides.

$$6y-3-18y=-23$$

Combine 6y and -18y to get -12y.

$$-12y-3=-23$$

Add 3 to both sides.

$$-12y=-23+3$$

Add -23 and 3 to get -20.

$$-12y=-20$$

Divide both sides by -12.

$$y=\frac{-20}{-12}$$

Reduce the fraction \frac{-20}{-12} to lowest terms by extracting and canceling out -4.

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