Solve the inequality and graph the solution.

Question

8<y+4
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( 8 < y + 4 \), we can isolate \( y \) by performing the following steps:

1. 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:

1. 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).

2. 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.

3. 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.