Question

1. |x - 3| = 9

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|a| = b\) (where \(b\geq0\)) means \(a = b\) or \(a=-b\). For \(|x - 3|=9\), we apply this definition.

Step2: Solve for \(x\) in two cases

• Case 1: \(x - 3=9\)

Add 3 to both sides: \(x=9 + 3=12\).

• Case 2: \(x - 3=-9\)

Add 3 to both sides: \(x=-9 + 3=-6\).

Answer:

\(x = 12\) or \(x=-6\)