To grasp the graph of the compound inequality x < 3 or x > 9, we first need to understand what the individual parts of this inequality mean. The compound inequality consists of two separate inequalities: x < 3 and x > 9.
1. Analyzing the first part: x < 3
This inequality means that any value of x that is less than 3 is included in the solution set. On a number line, this would be represented as a line extending to the left from the point 3, with an open circle at 3 to indicate that 3 itself is not included in the set.
2. Analyzing the second part: x > 9
This inequality indicates that any value of x greater than 9 is part of the solution as well. On the number line, this is shown as a line extending to the right from the point 9, with an open circle at 9, meaning that 9 is also not included in the solution set.
3. Combining the two parts
The overall graph for the compound inequality will consist of two distinct sections: one extending left from 3 and the other extending right from 9. Thus, the numbers represented on the graph will include everything less than 3 and everything greater than 9, with no overlap between the two sections.
4. Conclusion
To summarize, the graph of the compound inequality x < 3 or x > 9 will show two areas on the number line: a shaded region extending to the left of 3 (not including 3 itself) and another shaded region extending to the right of 9 (also not including 9). This visually conveys that any number less than 3 or greater than 9 is part of the solution set of the given compound inequality.