Solve gamma=k-R/3

$$\gamma = \frac { k - R } { 3 }$$

Solve for R

$$R=k-3\gamma$$

Steps for Solving Linear Equation

Divide each term of k-R by 3 to get \frac{1}{3}k-\frac{1}{3}R.

$$\gamma =\frac{1}{3}k-\frac{1}{3}R$$

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

$$\frac{1}{3}k-\frac{1}{3}R=\gamma$$

Subtract \frac{1}{3}k from both sides.

$$-\frac{1}{3}R=\gamma -\frac{1}{3}k$$

The equation is in standard form.

$$-\frac{1}{3}R=-\frac{k}{3}+\gamma$$

Multiply both sides by -3.

$$\frac{-\frac{1}{3}R}{-\frac{1}{3}}=\frac{-\frac{k}{3}+\gamma }{-\frac{1}{3}}$$

Dividing by -\frac{1}{3} undoes the multiplication by -\frac{1}{3}.

$$R=\frac{-\frac{k}{3}+\gamma }{-\frac{1}{3}}$$

Divide \gamma -\frac{k}{3} by -\frac{1}{3} by multiplying \gamma -\frac{k}{3} by the reciprocal of -\frac{1}{3}.

$$R=k-3\gamma$$

Solve for k

$$k=R+3\gamma$$

Steps for Solving Linear Equation

Divide each term of k-R by 3 to get \frac{1}{3}k-\frac{1}{3}R.

$$\gamma =\frac{1}{3}k-\frac{1}{3}R$$

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

$$\frac{1}{3}k-\frac{1}{3}R=\gamma$$

Add \frac{1}{3}R to both sides.

$$\frac{1}{3}k=\gamma +\frac{1}{3}R$$

The equation is in standard form.

$$\frac{1}{3}k=\frac{R}{3}+\gamma$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}k}{\frac{1}{3}}=\frac{\frac{R}{3}+\gamma }{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$k=\frac{\frac{R}{3}+\gamma }{\frac{1}{3}}$$

Divide \gamma +\frac{R}{3} by \frac{1}{3} by multiplying \gamma +\frac{R}{3} by the reciprocal of \frac{1}{3}.

$$k=R+3\gamma$$