Solve the inequality and graph the solution.

Question

12>q+9
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 \( 12 > q + 9 \), we first rearrange it to isolate \( q \):

\[ 12 - 9 > q \]

This simplifies to:

\[ 3 > q \]

or equivalently,

\[ q < 3 \]

This inequality indicates that \( q \) can take on any value less than 3.

Graphing the Solution:

1. Identifying the Endpoint: The endpoint of our inequality is 3. We'll plot this point on the number line.

2. Choosing Open or Closed: Since the inequality is strictly less than (\(<\)), we will draw an open circle at 3 to indicate that 3 is not included in the solution set.

3. Graphing the Ray: From the open circle at 3, we will shade the line to the left (towards smaller numbers) to represent all values less than 3.

Final Graph:

Here’s a simple representation of the graph:

<----(3)---------------->

In this graph:

• The circle at 3 is open (indicating that the value 3 itself is not included).
• The line extends to the left, covering all values less than 3.