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7\left(3x-2\right)+42\left(2x-1\right)=2\left(x+4\right)-14\left(x-1\right)
Multiply both sides of the equation by 14, the least common multiple of 2,7.
21x-14+42\left(2x-1\right)=2\left(x+4\right)-14\left(x-1\right)
Use the distributive property to multiply 7 by 3x-2.
21x-14+84x-42=2\left(x+4\right)-14\left(x-1\right)
Use the distributive property to multiply 42 by 2x-1.
105x-14-42=2\left(x+4\right)-14\left(x-1\right)
Combine 21x and 84x to get 105x.
105x-56=2\left(x+4\right)-14\left(x-1\right)
Subtract 42 from -14 to get -56.
105x-56=2x+8-14\left(x-1\right)
Use the distributive property to multiply 2 by x+4.
105x-56=2x+8-14x+14
Use the distributive property to multiply -14 by x-1.
105x-56=-12x+8+14
Combine 2x and -14x to get -12x.
105x-56=-12x+22
Add 8 and 14 to get 22.
105x-56+12x=22
Add 12x to both sides.
117x-56=22
Combine 105x and 12x to get 117x.
117x=22+56
Add 56 to both sides.
117x=78
Add 22 and 56 to get 78.
x=\frac{78}{117}
Divide both sides by 117.
x=\frac{2}{3}
Reduce the fraction \frac{78}{117} to lowest terms by extracting and canceling out 39.