Solve {2/7x+9/2-[(4-5x/7-3x+4/2)-frac{9}{14}x]}-1=frac{3}{2}x

$$\{ \frac { 2 } { 7 } x + \frac { 9 } { 2 } - [ ( \frac { 4 - 5 x } { 7 } - \frac { 3 x + 4 } { 2 } ) - \frac { 9 } { 14 } x ] \} - 1 = \frac { 3 } { 2 } x$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{4-5x}{7}-\frac{3x+4}{2}-\frac{9}{14}x\right)\right)-14=21x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 2 is 14. Multiply \frac{4-5x}{7} times \frac{2}{2}. Multiply \frac{3x+4}{2} times \frac{7}{7}.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{2\left(4-5x\right)}{14}-\frac{7\left(3x+4\right)}{14}-\frac{9}{14}x\right)\right)-14=21x$$

Since \frac{2\left(4-5x\right)}{14} and \frac{7\left(3x+4\right)}{14} have the same denominator, subtract them by subtracting their numerators.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{2\left(4-5x\right)-7\left(3x+4\right)}{14}-\frac{9}{14}x\right)\right)-14=21x$$

Do the multiplications in 2\left(4-5x\right)-7\left(3x+4\right).

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{8-10x-21x-28}{14}-\frac{9}{14}x\right)\right)-14=21x$$

Combine like terms in 8-10x-21x-28.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{-20-31x}{14}-\frac{9}{14}x\right)\right)-14=21x$$

To find the opposite of \frac{-20-31x}{14}-\frac{9}{14}x, find the opposite of each term.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\frac{-20-31x}{14}-\left(-\frac{9}{14}x\right)\right)-14=21x$$

The opposite of -\frac{9}{14}x is \frac{9}{14}x.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\frac{-20-31x}{14}+\frac{9}{14}x\right)-14=21x$$

Combine \frac{2}{7}x and \frac{9}{14}x to get \frac{13}{14}x.

$$14\left(\frac{13}{14}x+\frac{9}{2}-\frac{-20-31x}{14}\right)-14=21x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 14 is 14. Multiply \frac{9}{2} times \frac{7}{7}.

$$14\left(\frac{13}{14}x+\frac{9\times 7}{14}-\frac{-20-31x}{14}\right)-14=21x$$

Since \frac{9\times 7}{14} and \frac{-20-31x}{14} have the same denominator, subtract them by subtracting their numerators.

$$14\left(\frac{13}{14}x+\frac{9\times 7-\left(-20-31x\right)}{14}\right)-14=21x$$

Do the multiplications in 9\times 7-\left(-20-31x\right).

$$14\left(\frac{13}{14}x+\frac{63+20+31x}{14}\right)-14=21x$$

Combine like terms in 63+20+31x.

$$14\left(\frac{13}{14}x+\frac{83+31x}{14}\right)-14=21x$$

Use the distributive property to multiply 14 by \frac{13}{14}x+\frac{83+31x}{14}.

$$14\times \frac{13}{14}x+14\times \frac{83+31x}{14}-14=21x$$

Cancel out 14 and 14.

$$13x+14\times \frac{83+31x}{14}-14=21x$$

Express 14\times \frac{83+31x}{14} as a single fraction.

$$13x+\frac{14\left(83+31x\right)}{14}-14=21x$$

Cancel out 14 and 14.

$$13x+83+31x-14=21x$$

Combine 13x and 31x to get 44x.

$$44x+83-14=21x$$

Subtract 14 from 83 to get 69.

$$44x+69=21x$$

Subtract 21x from both sides.

$$44x+69-21x=0$$

Combine 44x and -21x to get 23x.

$$23x+69=0$$

Subtract 69 from both sides. Anything subtracted from zero gives its negation.

$$23x=-69$$

Divide both sides by 23.

$$x=\frac{-69}{23}$$

Divide -69 by 23 to get -3.

$$x=-3$$