Solve 1/3(-5/7m+6/7)=1-1/3m

$$\frac { 1 } { 3 } ( - \frac { 5 } { 7 } m + \frac { 6 } { 7 } ) = 1 - \frac { 1 } { 3 } m$$

Solve for m

$$m = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by -\frac{5}{7}m+\frac{6}{7}.

$$\frac{1}{3}\left(-\frac{5}{7}\right)m+\frac{1}{3}\times \frac{6}{7}=1-\frac{1}{3}m$$

Multiply \frac{1}{3} times -\frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-5\right)}{3\times 7}m+\frac{1}{3}\times \frac{6}{7}=1-\frac{1}{3}m$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{3\times 7}.

$$\frac{-5}{21}m+\frac{1}{3}\times \frac{6}{7}=1-\frac{1}{3}m$$

Fraction \frac{-5}{21} can be rewritten as -\frac{5}{21} by extracting the negative sign.

$$-\frac{5}{21}m+\frac{1}{3}\times \frac{6}{7}=1-\frac{1}{3}m$$

Multiply \frac{1}{3} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{21}m+\frac{1\times 6}{3\times 7}=1-\frac{1}{3}m$$

Do the multiplications in the fraction \frac{1\times 6}{3\times 7}.

$$-\frac{5}{21}m+\frac{6}{21}=1-\frac{1}{3}m$$

Reduce the fraction \frac{6}{21} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{21}m+\frac{2}{7}=1-\frac{1}{3}m$$

Add \frac{1}{3}m to both sides.

$$-\frac{5}{21}m+\frac{2}{7}+\frac{1}{3}m=1$$

Combine -\frac{5}{21}m and \frac{1}{3}m to get \frac{2}{21}m.

$$\frac{2}{21}m+\frac{2}{7}=1$$

Subtract \frac{2}{7} from both sides.

$$\frac{2}{21}m=1-\frac{2}{7}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{2}{21}m=\frac{7}{7}-\frac{2}{7}$$

Since \frac{7}{7} and \frac{2}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{21}m=\frac{7-2}{7}$$

Subtract 2 from 7 to get 5.

$$\frac{2}{21}m=\frac{5}{7}$$

Multiply both sides by \frac{21}{2}, the reciprocal of \frac{2}{21}.

$$m=\frac{5}{7}\times \frac{21}{2}$$

Multiply \frac{5}{7} times \frac{21}{2} by multiplying numerator times numerator and denominator times denominator.

$$m=\frac{5\times 21}{7\times 2}$$

Do the multiplications in the fraction \frac{5\times 21}{7\times 2}.

$$m=\frac{105}{14}$$

Reduce the fraction \frac{105}{14} to lowest terms by extracting and canceling out 7.

$$m=\frac{15}{2}$$