Solve x/m+a=c/d

$$\frac { x } { m } + a = \frac { c } { d }$$

Solve for a

$$a=\frac{cm-dx}{dm}$$

$$d\neq 0\text{ and }m\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by dm, the least common multiple of m,d.

$$dx+dma=mc$$

Subtract dx from both sides.

$$dma=mc-dx$$

The equation is in standard form.

$$dma=cm-dx$$

Divide both sides by dm.

$$\frac{dma}{dm}=\frac{cm-dx}{dm}$$

Dividing by dm undoes the multiplication by dm.

$$a=\frac{cm-dx}{dm}$$

Divide mc-dx by dm.

$$a=\frac{c}{d}-\frac{x}{m}$$

Solve for c

$$c=\frac{d\left(x+am\right)}{m}$$

$$m\neq 0\text{ and }d\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by dm, the least common multiple of m,d.

$$dx+dma=mc$$

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

$$mc=dx+dma$$

The equation is in standard form.

$$mc=dx+adm$$

Divide both sides by m.

$$\frac{mc}{m}=\frac{d\left(x+am\right)}{m}$$

Dividing by m undoes the multiplication by m.

$$c=\frac{d\left(x+am\right)}{m}$$