Solve 12-(4/3-7/9b)=8/3

$$12 - ( \frac { 4 } { 3 } - \frac { 7 } { 9 } b ) = \frac { 8 } { 3 }$$

Solve for b

$$b = -\frac{72}{7} = -10\frac{2}{7} \approx -10.285714286$$

Steps for Solving Linear Equation

To find the opposite of \frac{4}{3}-\frac{7}{9}b, find the opposite of each term.

$$12-\frac{4}{3}-\left(-\frac{7}{9}b\right)=\frac{8}{3}$$

The opposite of -\frac{7}{9}b is \frac{7}{9}b.

$$12-\frac{4}{3}+\frac{7}{9}b=\frac{8}{3}$$

Convert 12 to fraction \frac{36}{3}.

$$\frac{36}{3}-\frac{4}{3}+\frac{7}{9}b=\frac{8}{3}$$

Since \frac{36}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36-4}{3}+\frac{7}{9}b=\frac{8}{3}$$

Subtract 4 from 36 to get 32.

$$\frac{32}{3}+\frac{7}{9}b=\frac{8}{3}$$

Subtract \frac{32}{3} from both sides.

$$\frac{7}{9}b=\frac{8}{3}-\frac{32}{3}$$

Since \frac{8}{3} and \frac{32}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{9}b=\frac{8-32}{3}$$

Subtract 32 from 8 to get -24.

$$\frac{7}{9}b=\frac{-24}{3}$$

Divide -24 by 3 to get -8.

$$\frac{7}{9}b=-8$$

Multiply both sides by \frac{9}{7}, the reciprocal of \frac{7}{9}.

$$b=-8\times \frac{9}{7}$$

Express -8\times \frac{9}{7} as a single fraction.

$$b=\frac{-8\times 9}{7}$$

Multiply -8 and 9 to get -72.

$$b=\frac{-72}{7}$$

Fraction \frac{-72}{7} can be rewritten as -\frac{72}{7} by extracting the negative sign.

$$b=-\frac{72}{7}$$