Solve 1/3(x+1)-x=2/9

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

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

Steps for Solving Linear Equation

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

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

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

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

Subtract \frac{1}{3} from both sides.

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

Least common multiple of 9 and 3 is 9. Convert \frac{2}{9} and \frac{1}{3} to fractions with denominator 9.

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

Since \frac{2}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 2 to get -1.

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

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$x=-\frac{1}{9}\left(-\frac{3}{2}\right)$$

Multiply -\frac{1}{9} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-\left(-3\right)}{9\times 2}$$

Do the multiplications in the fraction \frac{-\left(-3\right)}{9\times 2}.

$$x=\frac{3}{18}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$x=\frac{1}{6}$$