Question

graph the solution to the inequality on the number line.
|u| < 7

Explanation:

Step1: Solve the absolute - value inequality

For the inequality \(|u|\lt7\), by the definition of absolute value (\(|x|\lt a\) is equivalent to \(-a\lt x\lt a\) when \(a\gt0\)), we have \(-7\lt u\lt7\).

Step2: Graph the solution on the number - line

On the number - line, we use an open circle at \(u = - 7\) (because \(u=-7\) is not included in the solution set \(-7\lt u\lt7\)) and an open circle at \(u = 7\) (because \(u = 7\) is not included in the solution set \(-7\lt u\lt7\)), and then shade the region between \(-7\) and \(7\).

Answer:

Graph an open circle at \(-7\), an open circle at \(7\), and shade the region between \(-7\) and \(7\) on the number - line.