Solve A=3/7y-1/5x-5/7y+5/10x

$$A = \frac { 3 } { 7 } y - \frac { 1 } { 5 } x - \frac { 5 } { 7 } y + \frac { 5 } { 10 } x$$

Solve for A

$$A=\frac{3x}{10}-\frac{2y}{7}$$

Solution Steps

Combine \frac{3}{7}y and -\frac{5}{7}y to get -\frac{2}{7}y.

$$A=-\frac{2}{7}y-\frac{1}{5}x+\frac{5}{10}x$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$A=-\frac{2}{7}y-\frac{1}{5}x+\frac{1}{2}x$$

Combine -\frac{1}{5}x and \frac{1}{2}x to get \frac{3}{10}x.

$$A=-\frac{2}{7}y+\frac{3}{10}x$$

Solve for x

$$x=\frac{10A}{3}+\frac{20y}{21}$$

Steps for Solving Linear Equation

Combine \frac{3}{7}y and -\frac{5}{7}y to get -\frac{2}{7}y.

$$A=-\frac{2}{7}y-\frac{1}{5}x+\frac{5}{10}x$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$A=-\frac{2}{7}y-\frac{1}{5}x+\frac{1}{2}x$$

Combine -\frac{1}{5}x and \frac{1}{2}x to get \frac{3}{10}x.

$$A=-\frac{2}{7}y+\frac{3}{10}x$$

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

$$-\frac{2}{7}y+\frac{3}{10}x=A$$

Add \frac{2}{7}y to both sides.

$$\frac{3}{10}x=A+\frac{2}{7}y$$

The equation is in standard form.

$$\frac{3}{10}x=\frac{2y}{7}+A$$

Divide both sides of the equation by \frac{3}{10}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{10}x}{\frac{3}{10}}=\frac{\frac{2y}{7}+A}{\frac{3}{10}}$$

Dividing by \frac{3}{10} undoes the multiplication by \frac{3}{10}.

$$x=\frac{\frac{2y}{7}+A}{\frac{3}{10}}$$

Divide A+\frac{2y}{7} by \frac{3}{10} by multiplying A+\frac{2y}{7} by the reciprocal of \frac{3}{10}.

$$x=\frac{10A}{3}+\frac{20y}{21}$$