To solve the inequality \( p + 6 < 10 \), we start by isolating \( p \):
- Subtract 6 from both sides:
\[ p < 10 - 6 \]
\[ p < 4 \]
This means that \( p \) can take any value that is less than 4. The solution is \( p \in (-\infty, 4) \).
Graphing the Solution
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Endpoints: The endpoint here is \( 4 \). Since the inequality is strict (it does not include 4), we represent it as an open circle at 4 on the number line.
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Select an Endpoint to Change from Closed to Open:
- We will use an open circle for the endpoint \( 4 \) (indicating that \( 4 \) is not included in the solution).
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Select the Middle of the Segment, Ray, or Line to Delete:
- The interval \( (-\infty, 4) \) goes to the left from 4 towards negative infinity, and we will shade that part of the number line indicating that all values less than 4 are included in the solution.
Final Representation
- The number line should look like this:
<---|----|----|----|----|----|----|----|----|----|----|----|---->
-2 -1 0 1 2 3 4 5 6
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- The open circle at \( 4 \) indicates that it is not included, and the arrow to the left indicates that all numbers less than \( 4 \) are part of the solution set.
Thus, the solution to the inequality \( p + 6 < 10 \) is \( p < 4 \), and the graph represents this accurately.