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1=5\left(3x-1\right)
Variable x cannot be equal to \frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 3x-1.
1=15x-5
Use the distributive property to multiply 5 by 3x-1.
15x-5=1
Swap sides so that all variable terms are on the left hand side.
15x=1+5
Add 5 to both sides.
15x=6
Add 1 and 5 to get 6.
x=\frac{6}{15}
Divide both sides by 15.
x=\frac{2}{5}
Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.