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

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{3} by x-9.

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

Express -\frac{1}{3}\left(-9\right) as a single fraction.

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

Multiply -1 and -9 to get 9.

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

Divide 9 by 3 to get 3.

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

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

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

Use the distributive property to multiply -\frac{1}{3} by \frac{2}{3}x+3.

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

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

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

Do the multiplications in the fraction \frac{-2}{3\times 3}.

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

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

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

Cancel out 3 and 3.

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

Combine x and -\frac{2}{9}x to get \frac{7}{9}x.

$$\frac{7}{9}x-1=\frac{1}{9}\left(x-9\right)+2$$

Use the distributive property to multiply \frac{1}{9} by x-9.

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{1}{9}\left(-9\right)+2$$

Multiply \frac{1}{9} and -9 to get \frac{-9}{9}.

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

Divide -9 by 9 to get -1.

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

Add -1 and 2 to get 1.

$$\frac{7}{9}x-1=\frac{1}{9}x+1$$

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

$$\frac{7}{9}x-1-\frac{1}{9}x=1$$

Combine \frac{7}{9}x and -\frac{1}{9}x to get \frac{2}{3}x.

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

Add 1 to both sides.

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

Add 1 and 1 to get 2.

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

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

$$x=2\times \frac{3}{2}$$

Cancel out 2 and 2.

$$x=3$$