Solve 5*1/3=1/3*3*k+1/3b

$$5 \cdot \frac { 1 } { 3 } = \frac { 1 } { 3 } \cdot 3 \cdot k + \frac { 1 } { 3 } b$$

Solve for b

$$b=5-3k$$

Steps for Solving Linear Equation

Multiply 5 and \frac{1}{3} to get \frac{5}{3}.

$$\frac{5}{3}=\frac{1}{3}\times 3k+\frac{1}{3}b$$

Multiply \frac{1}{3} and 3 to get 1.

$$\frac{5}{3}=k+\frac{1}{3}b$$

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

$$k+\frac{1}{3}b=\frac{5}{3}$$

Subtract k from both sides.

$$\frac{1}{3}b=\frac{5}{3}-k$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}b}{\frac{1}{3}}=\frac{\frac{5}{3}-k}{\frac{1}{3}}$$

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

$$b=\frac{\frac{5}{3}-k}{\frac{1}{3}}$$

Divide \frac{5}{3}-k by \frac{1}{3} by multiplying \frac{5}{3}-k by the reciprocal of \frac{1}{3}.

$$b=5-3k$$

Solve for k

$$k=\frac{5-b}{3}$$

Solution Steps

Multiply 5 and \frac{1}{3} to get \frac{5}{3}.

$$\frac{5}{3}=\frac{1}{3}\times 3k+\frac{1}{3}b$$

Multiply \frac{1}{3} and 3 to get 1.

$$\frac{5}{3}=k+\frac{1}{3}b$$

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

$$k+\frac{1}{3}b=\frac{5}{3}$$

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

$$k=\frac{5}{3}-\frac{1}{3}b$$