Solve 9x+7/2-(x-x-2/7)=36

$$\frac { 9 x + 7 } { 2 } - ( x - \frac { x - 2 } { 7 } ) = 36$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 14, the least common multiple of 2,7.

$$7\left(9x+7\right)-14\left(x-\frac{x-2}{7}\right)=504$$

Use the distributive property to multiply 7 by 9x+7.

$$63x+49-14\left(x-\frac{x-2}{7}\right)=504$$

Divide each term of x-2 by 7 to get \frac{1}{7}x-\frac{2}{7}.

$$63x+49-14\left(x-\left(\frac{1}{7}x-\frac{2}{7}\right)\right)=504$$

To find the opposite of \frac{1}{7}x-\frac{2}{7}, find the opposite of each term.

$$63x+49-14\left(x-\frac{1}{7}x-\left(-\frac{2}{7}\right)\right)=504$$

The opposite of -\frac{2}{7} is \frac{2}{7}.

$$63x+49-14\left(x-\frac{1}{7}x+\frac{2}{7}\right)=504$$

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

$$63x+49-14\left(\frac{6}{7}x+\frac{2}{7}\right)=504$$

Use the distributive property to multiply -14 by \frac{6}{7}x+\frac{2}{7}.

$$63x+49-14\times \frac{6}{7}x-14\times \frac{2}{7}=504$$

Express -14\times \frac{6}{7} as a single fraction.

$$63x+49+\frac{-14\times 6}{7}x-14\times \frac{2}{7}=504$$

Multiply -14 and 6 to get -84.

$$63x+49+\frac{-84}{7}x-14\times \frac{2}{7}=504$$

Divide -84 by 7 to get -12.

$$63x+49-12x-14\times \frac{2}{7}=504$$

Express -14\times \frac{2}{7} as a single fraction.

$$63x+49-12x+\frac{-14\times 2}{7}=504$$

Multiply -14 and 2 to get -28.

$$63x+49-12x+\frac{-28}{7}=504$$

Divide -28 by 7 to get -4.

$$63x+49-12x-4=504$$

Combine 63x and -12x to get 51x.

$$51x+49-4=504$$

Subtract 4 from 49 to get 45.

$$51x+45=504$$

Subtract 45 from both sides.

$$51x=504-45$$

Subtract 45 from 504 to get 459.

$$51x=459$$

Divide both sides by 51.

$$x=\frac{459}{51}$$

Divide 459 by 51 to get 9.

$$x=9$$