Solve x-1/3left(x-1/3left(x-9right)right)=1/9left(x-9right)

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

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

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

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

Multiply -1 and -9 to get 9.

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

Divide 9 by 3 to get 3.

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

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

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

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

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

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

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

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

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

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

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

Cancel out 3 and 3.

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

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

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

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

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

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

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

Divide -9 by 9 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 0.

$$\frac{2}{3}x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since \frac{2}{3} is not equal to 0, x must be equal to 0.

$$x=0$$