Question

Solve the inequality and graph the solution.
10w<20
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

First, let’s solve the inequality \(10w < 20\).

1. Divide both sides by 10:
\[
w < \frac{20}{10}
\]
Simplifying gives:
\[
w < 2
\]

Now, we will graph the solution \(w < 2\):

- The endpoint is at \(w = 2\).
- Since this is a strict inequality (less than, not less than or equal to), we represent this endpoint as an open circle on the graph.
- The solution includes all values **less than 2**, so we create a ray that extends to the left of the open circle.

Here's how we describe the graph:

1. **Plot the endpoint:**
- Plot an open circle at \(w = 2\).

2. **Change the endpoint from closed to open:**
- Since the inequality is strictly less than, we use an open circle at 2.

3. **Select the middle of the segment, ray, or line to delete it:**
- We delete the right segment starting from \(w = 2\) and going to the right since we are only looking for values less than 2.

The final graph will look like this:

```
<---(2)------------------>
```

where `(` denotes the open circle at 2, indicating that 2 is not included in the solution, and the arrow indicates all values less than 2.