Solve 2/3x+1/9=1/9x+1/3

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

Solve for x

$$x=\frac{2}{5}=0.4$$

Steps for Solving Linear Equation

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

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

Combine \frac{2}{3}x and -\frac{1}{9}x to get \frac{5}{9}x.

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

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

$$\frac{5}{9}x=\frac{1}{3}-\frac{1}{9}$$

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

$$\frac{5}{9}x=\frac{3}{9}-\frac{1}{9}$$

Since \frac{3}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{9}x=\frac{3-1}{9}$$

Subtract 1 from 3 to get 2.

$$\frac{5}{9}x=\frac{2}{9}$$

Multiply both sides by \frac{9}{5}, the reciprocal of \frac{5}{9}.

$$x=\frac{2}{9}\times \frac{9}{5}$$

Multiply \frac{2}{9} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{2\times 9}{9\times 5}$$

Cancel out 9 in both numerator and denominator.

$$x=\frac{2}{5}$$