Question

directions: solve and graph the following absolute

1. |x| ≤ 5

interval notation:

Explanation:

Step1: Solve the absolute - value inequality

For \(|x|\leq5\), by the definition of absolute value (\(|a|\leq b\) is equivalent to \(-b\leq a\leq b\)), we have \(- 5\leq x\leq5\).

Step2: Write in interval notation

The interval notation for \(-5\leq x\leq5\) is \([-5,5]\).

Answer:

The solution of the inequality \(|x|\leq5\) is \(-5\leq x\leq5\) and its interval notation is \([-5,5]\). On the number - line, we draw a solid circle at \(-5\) and \(5\) (because the inequality includes equality) and shade the region between them.