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5\times \frac{4}{5}=4x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.
4=4x
Cancel out 5 and 5.
4x=4
Swap sides so that all variable terms are on the left hand side.
x=\frac{4}{4}
Divide both sides by 4.
x=1
Divide 4 by 4 to get 1.