Solve a/3x+7=6/7x+2

$$\frac { a } { 3 x + 7 } = \frac { 6 } { 7 x + 2 }$$

Solve for a

$$a=\frac{6\left(3x+7\right)}{7x+2}$$

$$x\neq -\frac{7}{3}\text{ and }x\neq -\frac{2}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(3x+7\right)\left(7x+2\right), the least common multiple of 3x+7,7x+2.

$$\left(7x+2\right)a=\left(3x+7\right)\times 6$$

Use the distributive property to multiply 7x+2 by a.

$$7xa+2a=\left(3x+7\right)\times 6$$

Use the distributive property to multiply 3x+7 by 6.

$$7xa+2a=18x+42$$

Combine all terms containing a.

$$\left(7x+2\right)a=18x+42$$

Divide both sides by 7x+2.

$$\frac{\left(7x+2\right)a}{7x+2}=\frac{18x+42}{7x+2}$$

Dividing by 7x+2 undoes the multiplication by 7x+2.

$$a=\frac{18x+42}{7x+2}$$

Divide 18x+42 by 7x+2.

$$a=\frac{6\left(3x+7\right)}{7x+2}$$

Solve for x

$$x=-\frac{2\left(a-21\right)}{7a-18}$$

$$a\neq 0\text{ and }a\neq \frac{18}{7}$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{7}{3},-\frac{2}{7} since division by zero is not defined. Multiply both sides of the equation by \left(3x+7\right)\left(7x+2\right), the least common multiple of 3x+7,7x+2.

$$\left(7x+2\right)a=\left(3x+7\right)\times 6$$

Use the distributive property to multiply 7x+2 by a.

$$7xa+2a=\left(3x+7\right)\times 6$$

Use the distributive property to multiply 3x+7 by 6.

$$7xa+2a=18x+42$$

Subtract 18x from both sides.

$$7xa+2a-18x=42$$

Subtract 2a from both sides.

$$7xa-18x=42-2a$$

Combine all terms containing x.

$$\left(7a-18\right)x=42-2a$$

Divide both sides by 7a-18.

$$\frac{\left(7a-18\right)x}{7a-18}=\frac{42-2a}{7a-18}$$

Dividing by 7a-18 undoes the multiplication by 7a-18.

$$x=\frac{42-2a}{7a-18}$$

Divide 42-2a by 7a-18.

$$x=\frac{2\left(21-a\right)}{7a-18}$$

Variable x cannot be equal to any of the values -\frac{2}{7},-\frac{7}{3}.

$$x=\frac{2\left(21-a\right)}{7a-18}\text{, }x\neq -\frac{2}{7}\text{ and }x\neq -\frac{7}{3}$$