To graph the compound inequality [tex]\( x < 8.3 \)[/tex] or [tex]\( x > 9.8 \)[/tex], follow these steps:
1. Identify the two parts of the inequality:
- The first part is [tex]\( x < 8.3 \)[/tex].
- The second part is [tex]\( x > 9.8 \)[/tex].
2. Mark the critical points on the number line:
- Place a point at 8.3. Since [tex]\( x < 8.3 \)[/tex] does not include 8.3 itself, use an open circle to indicate that 8.3 is not part of the solution.
- Place another point at 9.8. Similarly, as [tex]\( x > 9.8 \)[/tex] does not include 9.8 itself, use an open circle to indicate that 9.8 is not part of the solution.
3. Shade the regions representing the solution:
- For [tex]\( x < 8.3 \)[/tex], shade the region to the left of 8.3 (all values less than 8.3).
- For [tex]\( x > 9.8 \)[/tex], shade the region to the right of 9.8 (all values greater than 9.8).
The number line will show two separate shaded regions:
- A shaded region extending infinitely to the left from 8.3, not including 8.3 itself.
- Another shaded region extending infinitely to the right from 9.8, not including 9.8 itself.
Thus, the graph on the number line of the compound inequality [tex]\( x < 8.3 \)[/tex] or [tex]\( x > 9.8 \)[/tex] comprises two distinct intervals:
- One interval from [tex]\(-\infty\)[/tex] to 8.3 (not including 8.3).
- Another interval from 9.8 to [tex]\(\infty\)[/tex] (not including 9.8).
