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81x+9x=10
Multiply both sides of the equation by 81, the least common multiple of 9,81.
90x=10
Combine 81x and 9x to get 90x.
x=\frac{10}{90}
Divide both sides by 90.
x=\frac{1}{9}
Reduce the fraction \frac{10}{90} to lowest terms by extracting and canceling out 10.