Question

1. |r| ≤ 3

Explanation:

Step1: Analyze the absolute - value inequality

The inequality \(|x|\leq3\) means that \(x\) is within a distance of \(3\) from \(0\) on the number line. Mathematically, it can be rewritten as \(- 3\leq x\leq3\).

Step2: Graph the solution on the number line

On the given number line, we mark the points \(-3\) and \(3\). Since the inequality is \(\leq\) (including equality), we use closed circles at \(-3\) and \(3\). Then we shade the region between \(-3\) and \(3\).

Answer:

The solution of the inequality \(|x|\leq3\) is \(-3\leq x\leq3\). On the number line, we have closed - circle at \(-3\) and \(3\) and the region between them is shaded.