Question

problem 1
click and drag to graph all the solutions to the inequality
|x| ≤ 3.

Explanation:

Step1: Solve the absolute - value inequality

The inequality \(|x|\leq3\) can be rewritten as \(- 3\leq x\leq3\). This is because if \(|x|\leq a\) (\(a\geq0\)), then \(-a\leq x\leq a\).

Step2: Interpret the solution on the number - line

On the number - line, we mark the points \(x = - 3\) and \(x = 3\) with closed circles (since the inequality includes equality, i.e., \(x=-3\) and \(x = 3\) are part of the solution set). Then we shade the region between \(x=-3\) and \(x = 3\).

Answer:

The solution of the inequality \(|x|\leq3\) is the set of all real numbers \(x\) such that \(-3\leq x\leq3\). On the number - line, we have closed circles at \(x=-3\) and \(x = 3\) with the line segment between them shaded.