Solve x+6/frac{28{5}}=y-4/frac{4{5}}

$$\frac { x + 6 } { \frac { 28 } { 5 } } = \frac { y - 4 } { \frac { 4 } { 5 } }$$

Solve for x

$$x=7y-34$$

Steps for Solving Linear Equation

Divide each term of x+6 by \frac{28}{5} to get \frac{x}{\frac{28}{5}}+\frac{6}{\frac{28}{5}}.

$$\frac{x}{\frac{28}{5}}+\frac{6}{\frac{28}{5}}=\frac{y-4}{\frac{4}{5}}$$

Divide 6 by \frac{28}{5} by multiplying 6 by the reciprocal of \frac{28}{5}.

$$\frac{x}{\frac{28}{5}}+6\times \frac{5}{28}=\frac{y-4}{\frac{4}{5}}$$

Multiply 6 and \frac{5}{28} to get \frac{15}{14}.

$$\frac{x}{\frac{28}{5}}+\frac{15}{14}=\frac{y-4}{\frac{4}{5}}$$

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

$$\frac{x}{\frac{28}{5}}+\frac{15}{14}=\frac{y}{\frac{4}{5}}+\frac{-4}{\frac{4}{5}}$$

Divide -4 by \frac{4}{5} by multiplying -4 by the reciprocal of \frac{4}{5}.

$$\frac{x}{\frac{28}{5}}+\frac{15}{14}=\frac{y}{\frac{4}{5}}-4\times \frac{5}{4}$$

Multiply -4 and \frac{5}{4} to get -5.

$$\frac{x}{\frac{28}{5}}+\frac{15}{14}=\frac{y}{\frac{4}{5}}-5$$

Subtract \frac{15}{14} from both sides.

$$\frac{x}{\frac{28}{5}}=\frac{y}{\frac{4}{5}}-5-\frac{15}{14}$$

Subtract \frac{15}{14} from -5 to get -\frac{85}{14}.

$$\frac{x}{\frac{28}{5}}=\frac{y}{\frac{4}{5}}-\frac{85}{14}$$

The equation is in standard form.

$$\frac{5}{28}x=\frac{5y}{4}-\frac{85}{14}$$

Divide both sides of the equation by \frac{5}{28}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{28}x}{\frac{5}{28}}=\frac{\frac{5y}{4}-\frac{85}{14}}{\frac{5}{28}}$$

Dividing by \frac{5}{28} undoes the multiplication by \frac{5}{28}.

$$x=\frac{\frac{5y}{4}-\frac{85}{14}}{\frac{5}{28}}$$

Divide \frac{5y}{4}-\frac{85}{14} by \frac{5}{28} by multiplying \frac{5y}{4}-\frac{85}{14} by the reciprocal of \frac{5}{28}.

$$x=7y-34$$

Solve for y

$$y=\frac{x+34}{7}$$

Steps for Solving Linear Equation

Divide each term of x+6 by \frac{28}{5} to get \frac{x}{\frac{28}{5}}+\frac{6}{\frac{28}{5}}.

$$\frac{x}{\frac{28}{5}}+\frac{6}{\frac{28}{5}}=\frac{y-4}{\frac{4}{5}}$$

Divide 6 by \frac{28}{5} by multiplying 6 by the reciprocal of \frac{28}{5}.

$$\frac{x}{\frac{28}{5}}+6\times \frac{5}{28}=\frac{y-4}{\frac{4}{5}}$$

Multiply 6 and \frac{5}{28} to get \frac{15}{14}.

$$\frac{x}{\frac{28}{5}}+\frac{15}{14}=\frac{y-4}{\frac{4}{5}}$$

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

$$\frac{x}{\frac{28}{5}}+\frac{15}{14}=\frac{y}{\frac{4}{5}}+\frac{-4}{\frac{4}{5}}$$

Divide -4 by \frac{4}{5} by multiplying -4 by the reciprocal of \frac{4}{5}.

$$\frac{x}{\frac{28}{5}}+\frac{15}{14}=\frac{y}{\frac{4}{5}}-4\times \frac{5}{4}$$

Multiply -4 and \frac{5}{4} to get -5.

$$\frac{x}{\frac{28}{5}}+\frac{15}{14}=\frac{y}{\frac{4}{5}}-5$$

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

$$\frac{y}{\frac{4}{5}}-5=\frac{x}{\frac{28}{5}}+\frac{15}{14}$$

Add 5 to both sides.

$$\frac{y}{\frac{4}{5}}=\frac{x}{\frac{28}{5}}+\frac{15}{14}+5$$

Add \frac{15}{14} and 5 to get \frac{85}{14}.

$$\frac{y}{\frac{4}{5}}=\frac{x}{\frac{28}{5}}+\frac{85}{14}$$

The equation is in standard form.

$$\frac{5}{4}y=\frac{5x}{28}+\frac{85}{14}$$

Divide both sides of the equation by \frac{5}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{4}y}{\frac{5}{4}}=\frac{\frac{5x}{28}+\frac{85}{14}}{\frac{5}{4}}$$

Dividing by \frac{5}{4} undoes the multiplication by \frac{5}{4}.

$$y=\frac{\frac{5x}{28}+\frac{85}{14}}{\frac{5}{4}}$$

Divide \frac{85}{14}+\frac{5x}{28} by \frac{5}{4} by multiplying \frac{85}{14}+\frac{5x}{28} by the reciprocal of \frac{5}{4}.

$$y=\frac{x+34}{7}$$