Solve 3a=-1+1/r

$$3 a = - 1 + \frac { 1 } { r }$$

Solve for a

$$a=-\frac{1}{3}+\frac{1}{3r}$$

$$r\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r.

$$3ar=r\left(-1\right)+1$$

The equation is in standard form.

$$3ra=1-r$$

Divide both sides by 3r.

$$\frac{3ra}{3r}=\frac{1-r}{3r}$$

Dividing by 3r undoes the multiplication by 3r.

$$a=\frac{1-r}{3r}$$

Divide -r+1 by 3r.

$$a=-\frac{1}{3}+\frac{1}{3r}$$

Solve for r

$$r=\frac{1}{3a+1}$$

$$a\neq -\frac{1}{3}$$

Steps for Solving Linear Equation

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

$$3ar=r\left(-1\right)+1$$

Subtract r\left(-1\right) from both sides.

$$3ar-r\left(-1\right)=1$$

Multiply -1 and -1 to get 1.

$$3ar+r=1$$

Combine all terms containing r.

$$\left(3a+1\right)r=1$$

Divide both sides by 3a+1.

$$\frac{\left(3a+1\right)r}{3a+1}=\frac{1}{3a+1}$$

Dividing by 3a+1 undoes the multiplication by 3a+1.

$$r=\frac{1}{3a+1}$$

Variable r cannot be equal to 0.

$$r=\frac{1}{3a+1}\text{, }r\neq 0$$