Final answer:
To solve the equation 1/2k + 6 = 4k - 8, subtract 1/2k from both sides, combine like terms, add 8 to both sides, combine constant terms, divide by 3.5, and solve for k to get k = 4.
Step-by-step explanation:
To solve the algebraic equation 1/2k + 6 = 4k - 8, we need to isolate the variable 'k' on one side of the equation. Here are the steps:
- Subtract 1/2k from both sides: 6 = 4k - 1/2k - 8.
- Combine like terms on the right side: 6 = 3.5k - 8.
- Add 8 to both sides to get all constant terms on the left side: 6 + 8 = 3.5k.
- Combine the constant terms: 14 = 3.5k.
- Divide both sides by 3.5 to solve for k: k = 14 / 3.5.
- Calculate the division: k = 4.
Therefore, the solution to the equation is k = 4.