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x^{-1}=\frac{5}{2}
Divide both sides by 2.
\frac{1}{x}=\frac{5}{2}
Reorder the terms.
2=5x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2.
5x=2
Swap sides so that all variable terms are on the left hand side.
x=\frac{2}{5}
Divide both sides by 5.