Question

solve the following inequality algebraically. |x + 6| > 6

Explanation:

Step1: Recall absolute value inequality rule

For \(|A| > B\) (where \(B>0\)), it is equivalent to \(A > B\) or \(A < -B\). Here, \(A = x + 6\) and \(B = 6\). So we have two cases:
Case 1: \(x + 6>6\)
Case 2: \(x + 6 < - 6\)

Step2: Solve Case 1

Subtract 6 from both sides of \(x + 6>6\):
\(x+6 - 6>6 - 6\)
\(x>0\)

Step3: Solve Case 2

Subtract 6 from both sides of \(x + 6 < - 6\):
\(x+6 - 6 < - 6 - 6\)
\(x < - 12\)

Answer:

The solution to the inequality \(|x + 6|>6\) is \(x < - 12\) or \(x>0\) (in interval notation, \((-\infty,-12)\cup(0,\infty)\))