Solve 2/3(x+y)=3(x+a)

$$\frac { 2 } { 3 } ( x + y ) = 3 ( x + a )$$

Solve for a

$$a=\frac{2y-7x}{9}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x+y.

$$\frac{2}{3}x+\frac{2}{3}y=3\left(x+a\right)$$

Use the distributive property to multiply 3 by x+a.

$$\frac{2}{3}x+\frac{2}{3}y=3x+3a$$

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

$$3x+3a=\frac{2}{3}x+\frac{2}{3}y$$

Subtract 3x from both sides.

$$3a=\frac{2}{3}x+\frac{2}{3}y-3x$$

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

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

The equation is in standard form.

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

Divide both sides by 3.

$$\frac{3a}{3}=\frac{2y-7x}{3\times 3}$$

Dividing by 3 undoes the multiplication by 3.

$$a=\frac{2y-7x}{3\times 3}$$

Divide \frac{-7x+2y}{3} by 3.

$$a=\frac{2y-7x}{9}$$

Solve for x

$$x=\frac{2y-9a}{7}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x+y.

$$\frac{2}{3}x+\frac{2}{3}y=3\left(x+a\right)$$

Use the distributive property to multiply 3 by x+a.

$$\frac{2}{3}x+\frac{2}{3}y=3x+3a$$

Subtract 3x from both sides.

$$\frac{2}{3}x+\frac{2}{3}y-3x=3a$$

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

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

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

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

The equation is in standard form.

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

Divide both sides of the equation by -\frac{7}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

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

Dividing by -\frac{7}{3} undoes the multiplication by -\frac{7}{3}.

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

Divide 3a-\frac{2y}{3} by -\frac{7}{3} by multiplying 3a-\frac{2y}{3} by the reciprocal of -\frac{7}{3}.

$$x=\frac{2y-9a}{7}$$