Solve 6/7(x+1/3)=4/3(x1/9)

$$\frac { 6 } { 7 } ( x + \frac { 1 } { 3 } ) = \frac { 4 } { 3 } ( x \frac { 1 } { 9 } )$$

Solve for x

$$x=-\frac{27}{67}\approx -0.402985075$$

Steps for Solving Linear Equation

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

$$\frac{6}{7}x+\frac{6}{7}\times \frac{1}{3}=\frac{4}{3}x\times \frac{1}{9}$$

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

$$\frac{6}{7}x+\frac{6\times 1}{7\times 3}=\frac{4}{3}x\times \frac{1}{9}$$

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

$$\frac{6}{7}x+\frac{6}{21}=\frac{4}{3}x\times \frac{1}{9}$$

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

$$\frac{6}{7}x+\frac{2}{7}=\frac{4}{3}x\times \frac{1}{9}$$

Multiply \frac{4}{3} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{7}x+\frac{2}{7}=\frac{4\times 1}{3\times 9}x$$

Do the multiplications in the fraction \frac{4\times 1}{3\times 9}.

$$\frac{6}{7}x+\frac{2}{7}=\frac{4}{27}x$$

Subtract \frac{4}{27}x from both sides.

$$\frac{6}{7}x+\frac{2}{7}-\frac{4}{27}x=0$$

Combine \frac{6}{7}x and -\frac{4}{27}x to get \frac{134}{189}x.

$$\frac{134}{189}x+\frac{2}{7}=0$$

Subtract \frac{2}{7} from both sides. Anything subtracted from zero gives its negation.

$$\frac{134}{189}x=-\frac{2}{7}$$

Multiply both sides by \frac{189}{134}, the reciprocal of \frac{134}{189}.

$$x=-\frac{2}{7}\times \frac{189}{134}$$

Multiply -\frac{2}{7} times \frac{189}{134} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-2\times 189}{7\times 134}$$

Do the multiplications in the fraction \frac{-2\times 189}{7\times 134}.

$$x=\frac{-378}{938}$$

Reduce the fraction \frac{-378}{938} to lowest terms by extracting and canceling out 14.

$$x=-\frac{27}{67}$$