Solve 13/2(7/3x+5/3)=-221/2

$$\frac { 13 } { 2 } ( \frac { 7 } { 3 } x + \frac { 5 } { 3 } ) = - \frac { 221 } { 2 }$$

Solve for x

$$x=-8$$

Steps for Solving Linear Equation

Multiply both sides by \frac{2}{13}, the reciprocal of \frac{13}{2}.

$$\frac{7}{3}x+\frac{5}{3}=-\frac{221}{2}\times \frac{2}{13}$$

Multiply -\frac{221}{2} times \frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{3}x+\frac{5}{3}=\frac{-221\times 2}{2\times 13}$$

Cancel out 2 in both numerator and denominator.

$$\frac{7}{3}x+\frac{5}{3}=\frac{-221}{13}$$

Divide -221 by 13 to get -17.

$$\frac{7}{3}x+\frac{5}{3}=-17$$

Subtract \frac{5}{3} from both sides.

$$\frac{7}{3}x=-17-\frac{5}{3}$$

Convert -17 to fraction -\frac{51}{3}.

$$\frac{7}{3}x=-\frac{51}{3}-\frac{5}{3}$$

Since -\frac{51}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{3}x=\frac{-51-5}{3}$$

Subtract 5 from -51 to get -56.

$$\frac{7}{3}x=-\frac{56}{3}$$

Multiply both sides by \frac{3}{7}, the reciprocal of \frac{7}{3}.

$$x=-\frac{56}{3}\times \frac{3}{7}$$

Multiply -\frac{56}{3} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-56\times 3}{3\times 7}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{-56}{7}$$

Divide -56 by 7 to get -8.

$$x=-8$$