Question

graph the solution to the inequality on the number line. |w + 6| ≥ 2

Explanation:

Step1: Split the absolute - value inequality

An absolute - value inequality \(|a|\geq b\) (\(b\geq0\)) can be split into two inequalities: \(a\geq b\) or \(a\leq - b\). Here \(a = w + 6\) and \(b = 2\), so we get \(w+6\geq2\) or \(w + 6\leq-2\).

Step2: Solve the first inequality

Solve \(w+6\geq2\). Subtract 6 from both sides: \(w+6 - 6\geq2 - 6\), which simplifies to \(w\geq - 4\).

Step3: Solve the second inequality

Solve \(w + 6\leq-2\). Subtract 6 from both sides: \(w+6 - 6\leq-2 - 6\), which simplifies to \(w\leq-8\).

Step4: Graph on the number line

On the number line, we draw a closed circle at \(w=-8\) (because \(w\) can equal \(-8\)) and shade to the left of \(-8\). We also draw a closed circle at \(w = - 4\) (because \(w\) can equal \(-4\)) and shade to the right of \(-4\).

Answer:

The solution of the inequality \(|w + 6|\geq2\) is \(w\leq-8\) or \(w\geq - 4\). On the number line, we have a closed - circle at \(w=-8\) with shading to the left and a closed - circle at \(w=-4\) with shading to the right.