Question

solve the equation,
2|k - 3| = 18

k = \boxed{} and \boxed{}

Explanation:

Step1: Divide both sides by 2

To isolate the absolute - value expression, we divide both sides of the equation \(2|k - 3|=18\) by 2.

$$ \frac{2|k - 3|}{2}=\frac{18}{2} $$

This simplifies to \(|k - 3| = 9\).

Step2: Solve the absolute - value equation

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

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

Add 3 to both sides of the equation:
\(k-3 + 3=9 + 3\)
\(k=12\)

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

Add 3 to both sides of the equation:
\(k-3 + 3=-9 + 3\)
\(k=-6\)

Answer:

\(k = 12\) and \(k=-6\)