Solve m=a+b+c/3

$$m = \frac { a + b + c } { 3 }$$

Solve for a

$$a=3m-b-c$$

Steps for Solving Linear Equation

Divide each term of a+b+c by 3 to get \frac{1}{3}a+\frac{1}{3}b+\frac{1}{3}c.

$$m=\frac{1}{3}a+\frac{1}{3}b+\frac{1}{3}c$$

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

$$\frac{1}{3}a+\frac{1}{3}b+\frac{1}{3}c=m$$

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

$$\frac{1}{3}a+\frac{1}{3}c=m-\frac{1}{3}b$$

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

$$\frac{1}{3}a=m-\frac{1}{3}b-\frac{1}{3}c$$

The equation is in standard form.

$$\frac{1}{3}a=-\frac{b}{3}-\frac{c}{3}+m$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}a}{\frac{1}{3}}=\frac{-\frac{b}{3}-\frac{c}{3}+m}{\frac{1}{3}}$$

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

$$a=\frac{-\frac{b}{3}-\frac{c}{3}+m}{\frac{1}{3}}$$

Divide m-\frac{b}{3}-\frac{c}{3} by \frac{1}{3} by multiplying m-\frac{b}{3}-\frac{c}{3} by the reciprocal of \frac{1}{3}.

$$a=3m-b-c$$

Solve for b

$$b=3m-a-c$$

Steps for Solving Linear Equation

Divide each term of a+b+c by 3 to get \frac{1}{3}a+\frac{1}{3}b+\frac{1}{3}c.

$$m=\frac{1}{3}a+\frac{1}{3}b+\frac{1}{3}c$$

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

$$\frac{1}{3}a+\frac{1}{3}b+\frac{1}{3}c=m$$

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

$$\frac{1}{3}b+\frac{1}{3}c=m-\frac{1}{3}a$$

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

$$\frac{1}{3}b=m-\frac{1}{3}a-\frac{1}{3}c$$

The equation is in standard form.

$$\frac{1}{3}b=-\frac{a}{3}-\frac{c}{3}+m$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}b}{\frac{1}{3}}=\frac{-\frac{a}{3}-\frac{c}{3}+m}{\frac{1}{3}}$$

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

$$b=\frac{-\frac{a}{3}-\frac{c}{3}+m}{\frac{1}{3}}$$

Divide m-\frac{a}{3}-\frac{c}{3} by \frac{1}{3} by multiplying m-\frac{a}{3}-\frac{c}{3} by the reciprocal of \frac{1}{3}.

$$b=3m-a-c$$