Solve x-1/3[x-1/3(x-9)]=1/9(x-4)

$$x - \frac { 1 } { 3 } [ x - \frac { 1 } { 3 } ( x - 9 ) ] = \frac { 1 } { 9 } ( x - 4 )$$

Solve for x

$$x=\frac{5}{6}\approx 0.833333333$$

Steps for Solving Linear Equation

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

$$x-\frac{1}{3}\left(x-\frac{1}{3}x-\frac{1}{3}\left(-9\right)\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+\frac{-\left(-9\right)}{3}\right)=\frac{1}{9}\left(x-4\right)$$

Multiply -1 and -9 to get 9.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+\frac{9}{3}\right)=\frac{1}{9}\left(x-4\right)$$

Divide 9 by 3 to get 3.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+3\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\left(\frac{2}{3}x+3\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\times \frac{2}{3}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

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

$$x+\frac{-2}{3\times 3}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

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

$$x+\frac{-2}{9}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{2}{9}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

Cancel out 3 and 3.

$$x-\frac{2}{9}x-1=\frac{1}{9}\left(x-4\right)$$

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

$$\frac{7}{9}x-1=\frac{1}{9}\left(x-4\right)$$

Use the distributive property to multiply \frac{1}{9} by x-4.

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{1}{9}\left(-4\right)$$

Multiply \frac{1}{9} and -4 to get \frac{-4}{9}.

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{-4}{9}$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{7}{9}x-1=\frac{1}{9}x-\frac{4}{9}$$

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

$$\frac{7}{9}x-1-\frac{1}{9}x=-\frac{4}{9}$$

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

$$\frac{2}{3}x-1=-\frac{4}{9}$$

Add 1 to both sides.

$$\frac{2}{3}x=-\frac{4}{9}+1$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{2}{3}x=-\frac{4}{9}+\frac{9}{9}$$

Since -\frac{4}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}x=\frac{-4+9}{9}$$

Add -4 and 9 to get 5.

$$\frac{2}{3}x=\frac{5}{9}$$

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

$$x=\frac{5}{9}\times \frac{3}{2}$$

Multiply \frac{5}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 3}{9\times 2}$$

Do the multiplications in the fraction \frac{5\times 3}{9\times 2}.

$$x=\frac{15}{18}$$

Reduce the fraction \frac{15}{18} to lowest terms by extracting and canceling out 3.

$$x=\frac{5}{6}$$