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14\left(3x+2\right)=13\left(5x-1\right)
Variable x cannot be equal to \frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by 14\left(5x-1\right), the least common multiple of 5x-1,14.
42x+28=13\left(5x-1\right)
Use the distributive property to multiply 14 by 3x+2.
42x+28=65x-13
Use the distributive property to multiply 13 by 5x-1.
42x+28-65x=-13
Subtract 65x from both sides.
-23x+28=-13
Combine 42x and -65x to get -23x.
-23x=-13-28
Subtract 28 from both sides.
-23x=-41
Subtract 28 from -13 to get -41.
x=\frac{-41}{-23}
Divide both sides by -23.
x=\frac{41}{23}
Fraction \frac{-41}{-23} can be simplified to \frac{41}{23} by removing the negative sign from both the numerator and the denominator.