Solve 6/4+5/6y=8/4x

$$\frac { 6 } { 4 } + \frac { 5 } { 6 } y = \frac { 8 } { 4 } x$$

Solve for x

$$x=\frac{5y}{12}+\frac{3}{4}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}+\frac{5}{6}y=\frac{8}{4}x$$

Divide 8 by 4 to get 2.

$$\frac{3}{2}+\frac{5}{6}y=2x$$

Swap sides so that all variable terms are on the left hand side.

$$2x=\frac{3}{2}+\frac{5}{6}y$$

The equation is in standard form.

$$2x=\frac{5y}{6}+\frac{3}{2}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\frac{5y}{6}+\frac{3}{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\frac{5y}{6}+\frac{3}{2}}{2}$$

Divide \frac{3}{2}+\frac{5y}{6} by 2.

$$x=\frac{5y}{12}+\frac{3}{4}$$

Solve for y

$$y=\frac{12x-9}{5}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}+\frac{5}{6}y=\frac{8}{4}x$$

Divide 8 by 4 to get 2.

$$\frac{3}{2}+\frac{5}{6}y=2x$$

Subtract \frac{3}{2} from both sides.

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

Divide both sides of the equation by \frac{5}{6}, which is the same as multiplying both sides by the reciprocal of the fraction.

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

Dividing by \frac{5}{6} undoes the multiplication by \frac{5}{6}.

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

Divide 2x-\frac{3}{2} by \frac{5}{6} by multiplying 2x-\frac{3}{2} by the reciprocal of \frac{5}{6}.

$$y=\frac{12x-9}{5}$$