To solve the inequality \( 8 < y + 4 \), we can isolate \( y \) by performing the following steps:
- Subtract 4 from both sides:
\[ 8 - 4 < y \implies 4 < y \]
This can be rewritten as:
\[ y > 4 \]
Now, we will address how to graph this solution:
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Identify Endpoints: The value \( y = 4 \) is an endpoint of the inequality, but because \( y \) must be greater than 4 (not equal), the endpoint will be open (not included in the solution).
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Graphing the Solution:
- On the number line, plot an open circle at \( 4 \) indicating that \( 4 \) itself is not included (since we have a "greater than" inequality).
- Shade the area to the right of \( 4 \) to indicate that all values greater than \( 4 \) are part of the solution.
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Visual Representation:
- The graph is an open circle at \( 4 \) (representing \( 4 \) is not included) and a ray extending to the right (representing all numbers greater than \( 4 \)).
Here’s a rough sketch of how the graph would look:
---o======================>
4
In this representation:
- The "o" at \( 4 \) is an open circle, indicating that 4 is not part of the solution set.
- The line extends indefinitely to the right, indicating all values greater than \( 4 \) are included in the solution.