Solve the inequality and graph the solution.

Question

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.