Question

1. solve each absolute value equation:

a. |x - 6| = 9

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|A| = B\) (where \(B\geq0\)) implies \(A = B\) or \(A=-B\). For \(|x - 6|=9\), we set up two equations: \(x - 6 = 9\) and \(x - 6=-9\).

Step2: Solve \(x - 6 = 9\)

Add 6 to both sides: \(x=9 + 6=15\).

Step3: Solve \(x - 6=-9\)

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

Answer:

\(x = 15\) or \(x=-3\)