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7\left(2\times 2+1\right)k=6
Multiply both sides of the equation by 14, the least common multiple of 2,7.
7\left(4+1\right)k=6
Multiply 2 and 2 to get 4.
7\times 5k=6
Add 4 and 1 to get 5.
35k=6
Multiply 7 and 5 to get 35.
k=\frac{6}{35}
Divide both sides by 35.