Question

graph the solution to the inequality on the number line.\\(|w + 2| > 8|\\)

Explanation:

Step1: Solve the absolute value inequality

The absolute value inequality \(|w + 2|>8\) means that \(w + 2>8\) or \(w + 2<-8\) (by the definition of absolute value inequalities: \(|x|>a\) implies \(x>a\) or \(x<-a\) for \(a>0\)).

Step2: Solve \(w + 2>8\)

Subtract 2 from both sides: \(w+2 - 2>8 - 2\), so \(w>6\).

Step3: Solve \(w + 2<-8\)

Subtract 2 from both sides: \(w+2 - 2<-8 - 2\), so \(w<-10\).

To graph this on the number line:

• For \(w<-10\), we draw an open circle at \(-10\) (since \(w\) is not equal to \(-10\)) and shade to the left.
• For \(w>6\), we draw an open circle at \(6\) (since \(w\) is not equal to \(6\)) and shade to the right.

Answer:

The solution to the inequality \(|w + 2|>8\) is \(w < - 10\) or \(w>6\). On the number line, there is an open circle at \(-10\) with shading to the left and an open circle at \(6\) with shading to the right.