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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
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{2\left(4-5x\right)}{14}-\frac{7\left(3x+4\right)}{14}-\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)-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{8-10x-21x-28}{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{-20-31x}{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}-\frac{-20-31x}{14}-\left(-\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}+\frac{9}{14}x\right)-14=21x
The opposite of -\frac{9}{14}x is \frac{9}{14}x.
14\left(\frac{13}{14}x+\frac{9}{2}-\frac{-20-31x}{14}\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\times 7}{14}-\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-\left(-20-31x\right)}{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{63+20+31x}{14}\right)-14=21x
Do the multiplications in 9\times 7-\left(-20-31x\right).
14\left(\frac{13}{14}x+\frac{83+31x}{14}\right)-14=21x
Combine like terms in 63+20+31x.
14\times \frac{13}{14}x+14\times \frac{83+31x}{14}-14=21x
Use the distributive property to multiply 14 by \frac{13}{14}x+\frac{83+31x}{14}.
13x+14\times \frac{83+31x}{14}-14=21x
Cancel out 14 and 14.
13x+\frac{14\left(83+31x\right)}{14}-14=21x
Express 14\times \frac{83+31x}{14} as a single fraction.
13x+83+31x-14=21x
Cancel out 14 and 14.
44x+83-14=21x
Combine 13x and 31x to get 44x.
44x+69=21x
Subtract 14 from 83 to get 69.
44x+69-21x=0
Subtract 21x from both sides.
23x+69=0
Combine 44x and -21x to get 23x.
23x=-69
Subtract 69 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-69}{23}
Divide both sides by 23.
x=-3
Divide -69 by 23 to get -3.