Final answer:
To find the value of k, distribute the fraction on the left side and simplify the equation step by step. Finally, divide by 79 to solve for k.
Step-by-step explanation:
To find the value of k, we need to simplify the given equation step by step:
- Start by distributing 5/4 to both terms inside the parentheses: 5/4 * (2-k) = 2(3k-1) - 2/3k
- Simplify each side of the equation: 10/4 - 5/4k = 6k - 2 - 2/3k
- Combine like terms on each side: -5/4k + 2/3k = 6k - 10/3
- Find a common denominator and combine k terms: (-15k + 8k)/12 = 6k - 10/3
- Simplify the k terms: -7k/12 = 6k - 10/3
- Multiply 12 on both sides to eliminate the denominator: -7k = 72k - 40/3
- Distribute -7 on the right side: -7k = 72k - 120/3
- Combine like terms: -7k = 72k - 40
- Add 7k to both sides: 0 = 79k - 40
- Add 40 to both sides: 40 = 79k
- Divide by 79: k = 40/79