Solve -1/9(x-27)+1/3(x+3)=x+67

$$- \frac { 1 } { 9 } ( x - 27 ) + \frac { 1 } { 3 } ( x + 3 ) = x + 67$$

Solve for x

$$x=-81$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{9} by x-27.

$$-\frac{1}{9}x-\frac{1}{9}\left(-27\right)+\frac{1}{3}\left(x+3\right)=x+67$$

Express -\frac{1}{9}\left(-27\right) as a single fraction.

$$-\frac{1}{9}x+\frac{-\left(-27\right)}{9}+\frac{1}{3}\left(x+3\right)=x+67$$

Multiply -1 and -27 to get 27.

$$-\frac{1}{9}x+\frac{27}{9}+\frac{1}{3}\left(x+3\right)=x+67$$

Divide 27 by 9 to get 3.

$$-\frac{1}{9}x+3+\frac{1}{3}\left(x+3\right)=x+67$$

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

$$-\frac{1}{9}x+3+\frac{1}{3}x+\frac{1}{3}\times 3=x+67$$

Cancel out 3 and 3.

$$-\frac{1}{9}x+3+\frac{1}{3}x+1=x+67$$

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

$$\frac{2}{9}x+3+1=x+67$$

Add 3 and 1 to get 4.

$$\frac{2}{9}x+4=x+67$$

Subtract x from both sides.

$$\frac{2}{9}x+4-x=67$$

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

$$-\frac{7}{9}x+4=67$$

Subtract 4 from both sides.

$$-\frac{7}{9}x=67-4$$

Subtract 4 from 67 to get 63.

$$-\frac{7}{9}x=63$$

Multiply both sides by -\frac{9}{7}, the reciprocal of -\frac{7}{9}.

$$x=63\left(-\frac{9}{7}\right)$$

Express 63\left(-\frac{9}{7}\right) as a single fraction.

$$x=\frac{63\left(-9\right)}{7}$$

Multiply 63 and -9 to get -567.

$$x=\frac{-567}{7}$$

Divide -567 by 7 to get -81.

$$x=-81$$