To find the value of k that satisfies the equation 7(7 - k) + 3k = -2(9k + 4) + 15, you can follow these steps:
1. Distribute the constants and variables on both sides of the equation:
7 * 7 - 7 * k + 3k = -2 * 9k - 2 * 4 + 15
2. Simplify both sides:
49 - 7k + 3k = -18k - 8 + 15
3. Combine like terms on each side:
(49 - 8) - 4k = -18k + 15
41 - 4k = -18k + 15
4. Move the variable terms to one side and the constant terms to the other side by adding 18k and subtracting 41 from both sides:
41 - 4k + 18k = 15
14k - 41 = 15
5. Add 41 to both sides to isolate the variable term:
14k = 15 + 41
14k = 56
6. Finally, divide by 14 to solve for k:
k = 56 / 14
k = 4
So, the value of k that satisfies the equation is k = 4.