Solve m+x/n=p

$$m + \frac { x } { n } = p$$

Solve for m

$$m=p-\frac{x}{n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n.

$$nm+x=pn$$

Subtract x from both sides.

$$nm=pn-x$$

The equation is in standard form.

$$nm=np-x$$

Divide both sides by n.

$$\frac{nm}{n}=\frac{np-x}{n}$$

Dividing by n undoes the multiplication by n.

$$m=\frac{np-x}{n}$$

Divide pn-x by n.

$$m=p-\frac{x}{n}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{x}{m-p}\text{, }&x\neq 0\text{ and }m\neq p\\n\neq 0\text{, }&m=p\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$nm+x=pn$$

Subtract pn from both sides.

$$nm+x-pn=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$nm-pn=-x$$

Combine all terms containing n.

$$\left(m-p\right)n=-x$$

Divide both sides by m-p.

$$\frac{\left(m-p\right)n}{m-p}=-\frac{x}{m-p}$$

Dividing by m-p undoes the multiplication by m-p.

$$n=-\frac{x}{m-p}$$

Variable n cannot be equal to 0.

$$n=-\frac{x}{m-p}\text{, }n\neq 0$$