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100\times 7=21x
Multiply both sides of the equation by 2100, the least common multiple of 21,100.
700=21x
Multiply 100 and 7 to get 700.
21x=700
Swap sides so that all variable terms are on the left hand side.
x=\frac{700}{21}
Divide both sides by 21.
x=\frac{100}{3}
Reduce the fraction \frac{700}{21} to lowest terms by extracting and canceling out 7.