Solve r=(b-a)m

$$r = ( b - a ) m$$

Solve for a

$$\left\{\begin{matrix}a=b-\frac{r}{m}\text{, }&m\neq 0\\a\in \mathrm{R}\text{, }&r=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply b-a by m.

$$r=bm-am$$

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

$$bm-am=r$$

Subtract bm from both sides.

$$-am=r-bm$$

The equation is in standard form.

$$\left(-m\right)a=r-bm$$

Divide both sides by -m.

$$\frac{\left(-m\right)a}{-m}=\frac{r-bm}{-m}$$

Dividing by -m undoes the multiplication by -m.

$$a=\frac{r-bm}{-m}$$

Divide r-bm by -m.

$$a=b-\frac{r}{m}$$

Solve for b

$$\left\{\begin{matrix}b=a+\frac{r}{m}\text{, }&m\neq 0\\b\in \mathrm{R}\text{, }&r=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply b-a by m.

$$r=bm-am$$

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

$$bm-am=r$$

Add am to both sides.

$$bm=r+am$$

The equation is in standard form.

$$mb=am+r$$

Divide both sides by m.

$$\frac{mb}{m}=\frac{am+r}{m}$$

Dividing by m undoes the multiplication by m.

$$b=\frac{am+r}{m}$$

Divide r+ma by m.

$$b=a+\frac{r}{m}$$