Solve 7/3(c+3)=1/3-c

$$\frac { 7 } { 3 } ( c + 3 ) = \frac { 1 } { 3 } - c$$

Solve for c

$$c=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{7}{3} by c+3.

$$\frac{7}{3}c+\frac{7}{3}\times 3=\frac{1}{3}-c$$

Cancel out 3 and 3.

$$\frac{7}{3}c+7=\frac{1}{3}-c$$

Add c to both sides.

$$\frac{7}{3}c+7+c=\frac{1}{3}$$

Combine \frac{7}{3}c and c to get \frac{10}{3}c.

$$\frac{10}{3}c+7=\frac{1}{3}$$

Subtract 7 from both sides.

$$\frac{10}{3}c=\frac{1}{3}-7$$

Convert 7 to fraction \frac{21}{3}.

$$\frac{10}{3}c=\frac{1}{3}-\frac{21}{3}$$

Since \frac{1}{3} and \frac{21}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}c=\frac{1-21}{3}$$

Subtract 21 from 1 to get -20.

$$\frac{10}{3}c=-\frac{20}{3}$$

Multiply both sides by \frac{3}{10}, the reciprocal of \frac{10}{3}.

$$c=-\frac{20}{3}\times \frac{3}{10}$$

Multiply -\frac{20}{3} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$c=\frac{-20\times 3}{3\times 10}$$

Cancel out 3 in both numerator and denominator.

$$c=\frac{-20}{10}$$

Divide -20 by 10 to get -2.

$$c=-2$$