Question

part 2 of 5 (b) the solution set for |w| > 0 is (-∞, 0) ∪ (0, ∞). part: 2 / 5 part 3 of 5 graph the solution set for |w| > 0. number line from -13 to 13

Explanation:

Step1: Understand the inequality

The inequality \(|w| > 0\) means that \(w\) can be any real number except \(0\), since the absolute value of a number is its distance from \(0\) on the number line, and we want all numbers whose distance from \(0\) is greater than \(0\).

Step2: Analyze the number line

On the number line, we need to represent all real numbers less than \(0\) (i.e., \((-\infty, 0)\)) and all real numbers greater than \(0\) (i.e., \((0, \infty)\)).

Step3: Graph the solution set

• For the interval \((-\infty, 0)\): We draw an open circle at \(0\) (because \(0\) is not included in the solution set) and draw an arrow pointing to the left (towards negative infinity) to represent all numbers less than \(0\).
• For the interval \((0, \infty)\): We draw an open circle at \(0\) (again, \(0\) is not included) and draw an arrow pointing to the right (towards positive infinity) to represent all numbers greater than \(0\).

Answer:

To graph the solution set for \(|w| > 0\):

1. Locate \(0\) on the number line.
2. Draw an open circle at \(0\) (since \(w = 0\) does not satisfy \(|w| > 0\)).
3. Draw an arrow starting from the open circle at \(0\) and pointing to the left (to represent all real numbers less than \(0\), i.e., \((-\infty, 0)\)).
4. Draw another arrow starting from the open circle at \(0\) and pointing to the right (to represent all real numbers greater than \(0\), i.e., \((0, \infty)\)).

Visually, this will look like two rays: one extending to the left from \(0\) (excluding \(0\)) and one extending to the right from \(0\) (excluding \(0\)) on the number line.