Solve 6/5x+1/9=7/3+2/3x

$$\frac{ 6 }{ 5 } x+ \frac{ 1 }{ 9 } = \frac{ 7 }{ 3 } + \frac{ 2 }{ 3 } x$$

Solve for x

$$x = \frac{25}{6} = 4\frac{1}{6} \approx 4.166666667$$

Steps for Solving Linear Equation

Subtract \frac{2}{3}x from both sides.

$$\frac{6}{5}x+\frac{1}{9}-\frac{2}{3}x=\frac{7}{3}$$

Combine \frac{6}{5}x and -\frac{2}{3}x to get \frac{8}{15}x.

$$\frac{8}{15}x+\frac{1}{9}=\frac{7}{3}$$

Subtract \frac{1}{9} from both sides.

$$\frac{8}{15}x=\frac{7}{3}-\frac{1}{9}$$

Least common multiple of 3 and 9 is 9. Convert \frac{7}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{8}{15}x=\frac{21}{9}-\frac{1}{9}$$

Since \frac{21}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{15}x=\frac{21-1}{9}$$

Subtract 1 from 21 to get 20.

$$\frac{8}{15}x=\frac{20}{9}$$

Multiply both sides by \frac{15}{8}, the reciprocal of \frac{8}{15}.

$$x=\frac{20}{9}\times \frac{15}{8}$$

Multiply \frac{20}{9} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{20\times 15}{9\times 8}$$

Do the multiplications in the fraction \frac{20\times 15}{9\times 8}.

$$x=\frac{300}{72}$$

Reduce the fraction \frac{300}{72} to lowest terms by extracting and canceling out 12.

$$x=\frac{25}{6}$$