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Question

Solve the inequality and graph the solution.
4w<8
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( 4w < 8 \), we start by isolating \( w \).

1. Divide both sides by 4: \[ w < \frac{8}{4} \] Simplifying gives: \[ w < 2 \]

Now we have the solution: \( w < 2 \).

Graphing the Solution

• Since we have a strict inequality (\(<\)), we will use an open circle (or open endpoint) at \( w = 2 \) to indicate that 2 is not included in the solution set.
• The solution is all values of \( w \) that are less than 2, which extends to the left on the number line.

The graph of the solution looks like this:

<———(2)—————>

Steps to Plot:

1. Plot the endpoint: Place an open circle at 2.
2. Select the endpoint to change: Since 2 is not included, it remains open.
3. Select the middle of the segment, ray, or line to delete it: Since the solution is \( w < 2 \), you will shade towards the left from 2 (indicating that all numbers less than 2 are included).

Summary

The solution to the inequality \( 4w < 8 \) is \( w < 2 \) with an open circle at 2, indicating that 2 is not part of the solution, and shading to the left to represent all values less than 2.