Question

solve the absolute value inequality. other than ∅, use interval notation graph the solution set on a number line.\\(|x + 5| > 0\\)\\(\bigcirc\\) bad question, c>0\\(\bigcirc\\) \\((-5, \infty)\\)\\(\bigcirc\\) \\((-\infty, -5) \cup (-5, \infty)\\)\\(\bigcirc\\) \\((-5, 5)\\)\\(\bigcirc\\) ∅

Explanation:

Step1: Recall absolute value property

The absolute value \(|a|\) is equal to \(a\) if \(a\geq0\) and \(-a\) if \(a < 0\), and \(|a|>0\) when \(a
eq0\). For \(|x + 5|>0\), this means \(x+5
eq0\).

Step2: Solve for \(x\)

Solve the equation \(x + 5=0\), we get \(x=- 5\). So \(x+5
eq0\) implies \(x
eq - 5\).

Step3: Write in interval notation

The set of all real numbers except \(x=-5\) can be written as \((-\infty,-5)\cup(-5,\infty)\).

Answer:

\((-\infty, - 5)\cup(-5, \infty)\) (corresponding to the option \((-\infty, -5)\cup(-5, \infty)\))