Answer: \(k = -\frac{1}{3}\)
Explanation:
To solve the equation \(28 - 7k = -7(7k + 2)\) for \(k\), follow these steps:
1. Distribute the -7 on the right side of the equation:
\(28 - 7k = -49k - 14\)
2. Move the terms with \(k\) to one side of the equation and the constant terms to the other side. You can do this by adding \(49k\) to both sides and subtracting 28 from both sides:
\(28 + 49k - 7k = -14\)
3. Simplify the equation:
\(42k = -14\)
4. Divide both sides by 42 to isolate \(k\):
\(\frac{42k}{42} = \frac{-14}{42}\)
\(k = \frac{-14}{42}\)
5. Simplify the fraction:
\(k = \frac{-7}{21}\)
So, the solution to the equation is \(k = -\frac{7}{21}\), which can be further simplified to \(k = -\frac{1}{3}\).