Question

solve the absolute value equation for k.\\
|-3k| + 6 = 15

Explanation:

Step1: Isolate the absolute value term

Subtract 6 from both sides of the equation \(|-3k| + 6 = 15\) to get \(|-3k|=15 - 6\).
\(|-3k| = 9\)

Step2: Solve the absolute value equation

The absolute value equation \(|a|=b\) (where \(b\geq0\)) has solutions \(a = b\) or \(a=-b\). So for \(|-3k| = 9\), we have two cases:

Case 1: \(-3k=9\)

Divide both sides by - 3: \(k=\frac{9}{-3}=-3\)

Case 2: \(-3k=-9\)

Divide both sides by - 3: \(k=\frac{-9}{-3}=3\)

Answer:

\(k = 3\) or \(k=-3\)