|x| - 2|x - 3| = \begin{cases} x - 6, & \text{if } x < 0 \\3x - 6, & \text{if } 0 \leq x < 3 \\-x + 6, & \text{if } x \geq 3 \end{cases}
1. For \(x < 0\):
|x| = -x \quad \text{and} \quad |x - 3| = -x + 3
-x - 2(-x + 3) = x - 6
2. For \(0 \leq x < 3\):
|x| = x \quad \text{and} \quad |x - 3| = -x + 3
x - 2(-x + 3) = 3x - 6
3. For \(x \geq 3\):
|x| = x \quad \text{and} \quad |x - 3| = x - 3
x - 2(x - 3) = -x + 6