Question

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graph all the solutions to the inequality: (|x|geq5)

Explanation:

Step1: Recall absolute - value inequality rule

If \(|x|\geq a\) (\(a > 0\)), then \(x\geq a\) or \(x\leq - a\). For \(|x|\geq5\), we have \(x\geq5\) or \(x\leq - 5\).

Step2: Graph on the number - line

On a number - line, we mark a closed circle at \(x = 5\) (because \(x\) can equal 5) and draw a ray to the right. We also mark a closed circle at \(x=-5\) (because \(x\) can equal - 5) and draw a ray to the left.

Answer:

The solution set is \(x\leq - 5\) or \(x\geq5\), which is represented on the number - line by closed circles at \(x=-5\) and \(x = 5\) with rays extending to the left from \(x=-5\) and to the right from \(x = 5\).