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70\left(3x-2\right)-21\left(4x-4\right)-350<-6\left(14-7x\right)
Multiply both sides of the equation by 210, the least common multiple of 3,10,35. Since 210 is positive, the inequality direction remains the same.
210x-140-21\left(4x-4\right)-350<-6\left(14-7x\right)
Use the distributive property to multiply 70 by 3x-2.
210x-140-84x+84-350<-6\left(14-7x\right)
Use the distributive property to multiply -21 by 4x-4.
126x-140+84-350<-6\left(14-7x\right)
Combine 210x and -84x to get 126x.
126x-56-350<-6\left(14-7x\right)
Add -140 and 84 to get -56.
126x-406<-6\left(14-7x\right)
Subtract 350 from -56 to get -406.
126x-406<-84+42x
Use the distributive property to multiply -6 by 14-7x.
126x-406-42x<-84
Subtract 42x from both sides.
84x-406<-84
Combine 126x and -42x to get 84x.
84x<-84+406
Add 406 to both sides.
84x<322
Add -84 and 406 to get 322.
x<\frac{322}{84}
Divide both sides by 84. Since 84 is positive, the inequality direction remains the same.
x<\frac{23}{6}
Reduce the fraction \frac{322}{84} to lowest terms by extracting and canceling out 14.