Solve 6-(2-x/4+3x/8)-9(5x/9+x/3)=2-x

$$6-(2- \frac{ x }{ 4 } +3 \frac{ x }{ 8 } )-9( \frac{ 5x }{ 9 } + \frac{ x }{ 3 } )=2-x$$

Solve for x

$$x=\frac{16}{57}\approx 0.280701754$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 72, the least common multiple of 4,8,9,3.

$$72\left(6-\left(2-\frac{x}{4}+3\times \frac{x}{8}\right)\right)-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

Express 3\times \frac{x}{8} as a single fraction.

$$72\left(6-\left(2-\frac{x}{4}+\frac{3x}{8}\right)\right)-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 8 is 8. Multiply \frac{x}{4} times \frac{2}{2}.

$$72\left(6-\left(2-\frac{2x}{8}+\frac{3x}{8}\right)\right)-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

Since -\frac{2x}{8} and \frac{3x}{8} have the same denominator, add them by adding their numerators.

$$72\left(6-\left(2+\frac{-2x+3x}{8}\right)\right)-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

Combine like terms in -2x+3x.

$$72\left(6-\left(2+\frac{x}{8}\right)\right)-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

To find the opposite of 2+\frac{x}{8}, find the opposite of each term.

$$72\left(6-2-\frac{x}{8}\right)-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

Subtract 2 from 6 to get 4.

$$72\left(4-\frac{x}{8}\right)-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

Use the distributive property to multiply 72 by 4-\frac{x}{8}.

$$288-72\times \frac{x}{8}-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

Cancel out 8, the greatest common factor in 72 and 8.

$$288-9x-648\left(\frac{5x}{9}+\frac{x}{3}\right)=144-72x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 3 is 9. Multiply \frac{x}{3} times \frac{3}{3}.

$$288-9x-648\left(\frac{5x}{9}+\frac{3x}{9}\right)=144-72x$$

Since \frac{5x}{9} and \frac{3x}{9} have the same denominator, add them by adding their numerators.

$$288-9x-648\times \frac{5x+3x}{9}=144-72x$$

Combine like terms in 5x+3x.

$$288-9x-648\times \frac{8x}{9}=144-72x$$

Cancel out 9, the greatest common factor in 648 and 9.

$$288-9x-72\times 8x=144-72x$$

Multiply 72 and 8 to get 576.

$$288-9x-576x=144-72x$$

Combine -9x and -576x to get -585x.

$$288-585x=144-72x$$

Add 72x to both sides.

$$288-585x+72x=144$$

Combine -585x and 72x to get -513x.

$$288-513x=144$$

Subtract 288 from both sides.

$$-513x=144-288$$

Subtract 288 from 144 to get -144.

$$-513x=-144$$

Divide both sides by -513.

$$x=\frac{-144}{-513}$$

Reduce the fraction \frac{-144}{-513} to lowest terms by extracting and canceling out -9.

$$x=\frac{16}{57}$$