Solve x+3cm/9m=x-1m/6m

$$\frac{ x+3cm }{ 9m } = \frac{ x-1m }{ 6m }$$

Solve for c

$$c=\frac{x}{6m}-\frac{1}{2}$$

$$m\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18m, the least common multiple of 9m,6m.

$$2\left(x+3cm\right)=3\left(x-m\right)$$

Use the distributive property to multiply 2 by x+3cm.

$$2x+6cm=3\left(x-m\right)$$

Use the distributive property to multiply 3 by x-m.

$$2x+6cm=3x-3m$$

Subtract 2x from both sides.

$$6cm=3x-3m-2x$$

Combine 3x and -2x to get x.

$$6cm=x-3m$$

The equation is in standard form.

$$6mc=x-3m$$

Divide both sides by 6m.

$$\frac{6mc}{6m}=\frac{x-3m}{6m}$$

Dividing by 6m undoes the multiplication by 6m.

$$c=\frac{x-3m}{6m}$$

Divide x-3m by 6m.

$$c=\frac{x}{6m}-\frac{1}{2}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{x}{3\left(2c+1\right)}\text{, }&x\neq 0\text{ and }c\neq -\frac{1}{2}\\m\neq 0\text{, }&x=0\text{ and }c=-\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 18m, the least common multiple of 9m,6m.

$$2\left(x+3cm\right)=3\left(x-m\right)$$

Use the distributive property to multiply 2 by x+3cm.

$$2x+6mc=3\left(x-m\right)$$

Use the distributive property to multiply 3 by x-m.

$$2x+6mc=3x-3m$$

Add 3m to both sides.

$$2x+6mc+3m=3x$$

Subtract 2x from both sides.

$$6mc+3m=3x-2x$$

Combine 3x and -2x to get x.

$$6mc+3m=x$$

Combine all terms containing m.

$$\left(6c+3\right)m=x$$

Divide both sides by 6c+3.

$$\frac{\left(6c+3\right)m}{6c+3}=\frac{x}{6c+3}$$

Dividing by 6c+3 undoes the multiplication by 6c+3.

$$m=\frac{x}{6c+3}$$

Divide x by 6c+3.

$$m=\frac{x}{3\left(2c+1\right)}$$

Variable m cannot be equal to 0.

$$m=\frac{x}{3\left(2c+1\right)}\text{, }m\neq 0$$