Solve 12(3x/4-x/3)-18(7/9x-5/6x)=x-5

$$12 ( \frac { 3 x } { 4 } - \frac { x } { 3 } ) - 18 ( \frac { 7 } { 9 } x - \frac { 5 } { 6 } x ) = x - 5$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 4,3,9,6.

$$432\left(\frac{3x}{4}-\frac{x}{3}\right)-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{3x}{4} times \frac{3}{3}. Multiply \frac{x}{3} times \frac{4}{4}.

$$432\left(\frac{3\times 3x}{12}-\frac{4x}{12}\right)-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Since \frac{3\times 3x}{12} and \frac{4x}{12} have the same denominator, subtract them by subtracting their numerators.

$$432\times \frac{3\times 3x-4x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Do the multiplications in 3\times 3x-4x.

$$432\times \frac{9x-4x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Combine like terms in 9x-4x.

$$432\times \frac{5x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Cancel out 12, the greatest common factor in 432 and 12.

$$36\times 5x-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Combine \frac{7}{9}x and -\frac{5}{6}x to get -\frac{1}{18}x.

$$36\times 5x-648\left(-\frac{1}{18}\right)x=36x-180$$

Express 648\left(-\frac{1}{18}\right) as a single fraction.

$$36\times 5x-\frac{648\left(-1\right)}{18}x=36x-180$$

Multiply 648 and -1 to get -648.

$$36\times 5x-\frac{-648}{18}x=36x-180$$

Divide -648 by 18 to get -36.

$$36\times 5x-\left(-36x\right)=36x-180$$

The opposite of -36x is 36x.

$$36\times 5x+36x=36x-180$$

Multiply 36 and 5 to get 180.

$$180x+36x=36x-180$$

Combine 180x and 36x to get 216x.

$$216x=36x-180$$

Subtract 36x from both sides.

$$216x-36x=-180$$

Combine 216x and -36x to get 180x.

$$180x=-180$$

Divide both sides by 180.

$$x=\frac{-180}{180}$$

Divide -180 by 180 to get -1.

$$x=-1$$