Question

solve for k.
\\(\frac{-2}{k - 5} = \frac{8}{k + 5}\\)

Explanation:

Step1: Cross - multiply the fractions

To solve the equation \(\frac{-2}{k - 5}=\frac{8}{k + 5}\), we cross - multiply. Cross - multiplying gives us \(-2(k + 5)=8(k - 5)\).

Step2: Distribute the numbers

Distribute \(-2\) on the left side and \(8\) on the right side. We get \(-2k-10 = 8k-40\).

Step3: Move the variable terms to one side

Add \(2k\) to both sides of the equation to get all the \(k\) terms on one side. \(-2k + 2k-10=8k + 2k-40\), which simplifies to \(-10 = 10k-40\).

Step4: Move the constant terms to the other side

Add \(40\) to both sides of the equation. \(-10 + 40=10k-40 + 40\), which simplifies to \(30 = 10k\).

Step5: Solve for k

Divide both sides of the equation by \(10\). \(\frac{30}{10}=\frac{10k}{10}\), so \(k = 3\).

Answer:

\(k = 3\)