Solve 1/6(x+6)+1/18(x-18)=x+14

$$\frac { 1 } { 6 } ( x + 6 ) + \frac { 1 } { 18 } ( x - 18 ) = x + 14$$

Solve for x

$$x=-18$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{6} by x+6.

$$\frac{1}{6}x+\frac{1}{6}\times 6+\frac{1}{18}\left(x-18\right)=x+14$$

Cancel out 6 and 6.

$$\frac{1}{6}x+1+\frac{1}{18}\left(x-18\right)=x+14$$

Use the distributive property to multiply \frac{1}{18} by x-18.

$$\frac{1}{6}x+1+\frac{1}{18}x+\frac{1}{18}\left(-18\right)=x+14$$

Multiply \frac{1}{18} and -18 to get \frac{-18}{18}.

$$\frac{1}{6}x+1+\frac{1}{18}x+\frac{-18}{18}=x+14$$

Divide -18 by 18 to get -1.

$$\frac{1}{6}x+1+\frac{1}{18}x-1=x+14$$

Combine \frac{1}{6}x and \frac{1}{18}x to get \frac{2}{9}x.

$$\frac{2}{9}x+1-1=x+14$$

Subtract 1 from 1 to get 0.

$$\frac{2}{9}x=x+14$$

Subtract x from both sides.

$$\frac{2}{9}x-x=14$$

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

$$-\frac{7}{9}x=14$$

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

$$x=14\left(-\frac{9}{7}\right)$$

Express 14\left(-\frac{9}{7}\right) as a single fraction.

$$x=\frac{14\left(-9\right)}{7}$$

Multiply 14 and -9 to get -126.

$$x=\frac{-126}{7}$$

Divide -126 by 7 to get -18.

$$x=-18$$