Question

(b) the solution set in interval notation for |w - 2| > 0 is (-∞, 2) ∪ (2, ∞). part: 2 / 4 part 3 of 4 graph the solution set for |w - 2| > 0.

Explanation:

Step1: Analyze the inequality

The inequality \(|w - 2|>0\) means that the distance between \(w\) and \(2\) on the number line is greater than \(0\). This implies that \(w\) cannot be equal to \(2\) (because the distance from a number to itself is \(0\)). So \(w\) can be any real number except \(2\).

Step2: Graph the solution

• First, draw a number line.
• Mark the point \(2\) on the number line. Since \(w

eq2\), we use an open circle (hollow dot) at \(2\) to indicate that \(2\) is not included in the solution set.

• Then, we shade the regions to the left of \(2\) (which represents all numbers less than \(2\), i.e., the interval \((-\infty, 2)\)) and to the right of \(2\) (which represents all numbers greater than \(2\), i.e., the interval \((2, \infty)\)).

Answer:

To graph the solution set for \(|w - 2|>0\):

1. Draw a horizontal number line.
2. Place an open circle (hollow dot) at \(w = 2\) (because \(w = 2\) does not satisfy \(|w - 2|>0\) as \(|2 - 2|=0\) which is not greater than \(0\)).
3. Shade the entire number line to the left of \(2\) (representing \(w<2\)) and to the right of \(2\) (representing \(w > 2\)).