Question

question
solve the following inequality algebraically.
|x + 2| > 10
answer attempt 1 out of 2

Explanation:

Step1: Recall absolute value inequality rule

For \(|A| > B\) (where \(B>0\)), it is equivalent to \(A > B\) or \(A < -B\). Here, \(A = x + 2\) and \(B = 10\), so we have two inequalities: \(x + 2>10\) or \(x + 2 < - 10\).

Step2: Solve \(x + 2>10\)

Subtract 2 from both sides: \(x+2 - 2>10 - 2\), which simplifies to \(x>8\).

Step3: Solve \(x + 2 < - 10\)

Subtract 2 from both sides: \(x+2 - 2 < - 10 - 2\), which simplifies to \(x < - 12\).

Answer:

\(x < - 12\) or \(x>8\) (in interval notation: \((-\infty, - 12)\cup(8, \infty)\))