Question

1. |x + 9| = 7

Explanation:

Step1: Apply absolute value definition

If \(|A| = B\) (\(B\geq0\)), then \(A = B\) or \(A=-B\). So for \(|x + 9|=7\), we have two cases:
Case 1: \(x + 9 = 7\)
Case 2: \(x + 9=-7\)

Step2: Solve Case 1

Subtract 9 from both sides of \(x + 9 = 7\):
\(x=7 - 9=-2\)

Step3: Solve Case 2

Subtract 9 from both sides of \(x + 9=-7\):
\(x=-7 - 9=-16\)

Answer:

\(x = -2\) or \(x=-16\)