Solve 5/6y-1/4=1-2/3y

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

Solve for y

$$y = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12y, the least common multiple of 6y,4,3y.

$$2\times 5+12y\left(-\frac{1}{4}\right)=12y-4\times 2$$

Multiply 2 and 5 to get 10.

$$10+12y\left(-\frac{1}{4}\right)=12y-4\times 2$$

Multiply 12 and -\frac{1}{4} to get -3.

$$10-3y=12y-4\times 2$$

Multiply -4 and 2 to get -8.

$$10-3y=12y-8$$

Subtract 12y from both sides.

$$10-3y-12y=-8$$

Combine -3y and -12y to get -15y.

$$10-15y=-8$$

Subtract 10 from both sides.

$$-15y=-8-10$$

Subtract 10 from -8 to get -18.

$$-15y=-18$$

Divide both sides by -15.

$$y=\frac{-18}{-15}$$

Reduce the fraction \frac{-18}{-15} to lowest terms by extracting and canceling out -3.

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