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

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

Solve for x

$$x = -\frac{459}{5} = -91\frac{4}{5} = -91.8$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply -14 and 6 to get -84.

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

Divide -84 by 7 to get -12.

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

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

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

Multiply -14 and 2 to get -28.

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

Divide -28 by 7 to get -4.

$$7x+49-12x-4=504$$

Combine 7x and -12x to get -5x.

$$-5x+49-4=504$$

Subtract 4 from 49 to get 45.

$$-5x+45=504$$

Subtract 45 from both sides.

$$-5x=504-45$$

Subtract 45 from 504 to get 459.

$$-5x=459$$

Divide both sides by -5.

$$x=\frac{459}{-5}$$

Fraction \frac{459}{-5} can be rewritten as -\frac{459}{5} by extracting the negative sign.

$$x=-\frac{459}{5}$$