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10\times \frac{25}{100}x=110\times 2.5x
Multiply both sides of the equation by 220, the least common multiple of 220,2.
10\times \frac{1}{4}x=110\times 2.5x
Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.
\frac{10}{4}x=110\times 2.5x
Multiply 10 and \frac{1}{4} to get \frac{10}{4}.
\frac{5}{2}x=110\times 2.5x
Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.
\frac{5}{2}x=275x
Multiply 110 and 2.5 to get 275.
\frac{5}{2}x-275x=0
Subtract 275x from both sides.
-\frac{545}{2}x=0
Combine \frac{5}{2}x and -275x to get -\frac{545}{2}x.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since -\frac{545}{2} is not equal to 0, x must be equal to 0.