Question

question
solve the following inequality algebraically.
|x + 6| > 6
answer attempt 1 out of 2
submit answer
∅ or ∪ ∞ < > ≤ ≥ , ,) (,
all real numbers

Explanation:

Step1: Apply 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 get two inequalities: \(x + 6>6\) or \(x + 6 < - 6\).

Step2: Solve \(x + 6>6\)

Subtract 6 from both sides: \(x+6 - 6>6 - 6\), which simplifies to \(x>0\).

Step3: Solve \(x + 6 < - 6\)

Subtract 6 from both sides: \(x+6 - 6 < - 6 - 6\), which simplifies to \(x < - 12\).

Step4: Combine the solutions

The solution to the inequality \(|x + 6|>6\) is the union of the solutions to the two inequalities, so \(x < - 12\) or \(x>0\), which in interval notation is \((-\infty, - 12)\cup(0, \infty)\).

Answer:

\(x < - 12\) or \(x>0\) (or in interval notation \((-\infty, - 12)\cup(0, \infty)\))