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-21=10\left(1\times 6+1\right)r
Multiply both sides of the equation by 60, the least common multiple of 20,6.
-21=10\left(6+1\right)r
Multiply 1 and 6 to get 6.
-21=10\times 7r
Add 6 and 1 to get 7.
-21=70r
Multiply 10 and 7 to get 70.
70r=-21
Swap sides so that all variable terms are on the left hand side.
r=\frac{-21}{70}
Divide both sides by 70.
r=-\frac{3}{10}
Reduce the fraction \frac{-21}{70} to lowest terms by extracting and canceling out 7.