Final answer:
To solve for K in the equation 1/3k -1/2=6+3/7, the constants on the right side of the equation are combined. After simplifying, the equation becomes 1/3k = 83/14. Multiplying both sides by 3 gives K = 249/14, which is not one of the provided options.
Step-by-step explanation:
To solve for K in the equation 1/3k -1/2=6+3/7, we first combine the constants on the right side of the equation. The common denominator for 2 and 7 is 14, so we convert -1/2 to -7/14 and 6 to 84/14 (because 6×14=84), and 3/7 to 6/14. The equation now reads 1/3k = 84/14 + 6/14 - 7/14.
Next, we add the fractions on the right side to get 1/3k = 83/14, which simplifies to 1/3k = 83/14. To solve for K, we multiply both sides by 3 to get K = 3 × (83/14), which simplifies to K = 249/14. None of the options A) 7/6 B) 13/6 C) 5/6 D) 1/6 are correct.