Question

graph the solution to the inequality on the number line. |x| > 6

Explanation:

Step1: Recall absolute - value rule

If \(|x|>a\) (\(a > 0\)), then \(x>a\) or \(x < - a\). Here \(a = 6\), so \(x>6\) or \(x<-6\).

Step2: Graph on number - line

On the number - line, we use open circles at \(x=-6\) and \(x = 6\) (since the inequality is strict, \(x
eq\pm6\)). Then we shade the regions to the left of \(x=-6\) and to the right of \(x = 6\).

Answer:

On the number - line, place open circles at \(x=-6\) and \(x = 6\). Shade the part of the number - line to the left of \(x=-6\) and to the right of \(x = 6\).