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10k+2\left(1\times 5+3\right)=2\times 10+7
Multiply both sides of the equation by 10, the least common multiple of 5,10.
10k+2\left(5+3\right)=2\times 10+7
Multiply 1 and 5 to get 5.
10k+2\times 8=2\times 10+7
Add 5 and 3 to get 8.
10k+16=2\times 10+7
Multiply 2 and 8 to get 16.
10k+16=20+7
Multiply 2 and 10 to get 20.
10k+16=27
Add 20 and 7 to get 27.
10k=27-16
Subtract 16 from both sides.
10k=11
Subtract 16 from 27 to get 11.
k=\frac{11}{10}
Divide both sides by 10.