The graph of the compound inequality can be described by examining each part of the inequality separately.
First, let’s break down the inequalities:
- x < 3: This part indicates that all values of x that are less than 3 will be included in the graph.
- x > 9: This part indicates that all values of x greater than 9 will also be included.
- x < 5: This states that all values of x less than 5 should be included in the graph.
- x > 10: Finally, this indicates that we should also include all values of x that are greater than 10.
Now, since we are dealing with the compound inequality connected by ‘or’, the graph will include all regions defined by these inequalities. Therefore, we are looking at:
- All values left of 3, as well as values between 5 and 9, and all values greater than 10.
This results in an overall graph that has three distinct parts: one continuous line to the left of 3, another continuous line between 5 and 9, and a third continuous line starting above 10.
In conclusion, the graph of the compound inequality will be made up of three separate sections on the number line, creating gaps in the areas between 3 and 5 and between 9 and 10.