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16x=9\times 100
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9x, the least common multiple of 9,x.
16x=900
Multiply 9 and 100 to get 900.
x=\frac{900}{16}
Divide both sides by 16.
x=\frac{225}{4}
Reduce the fraction \frac{900}{16} to lowest terms by extracting and canceling out 4.