Solve the inequality and graph the solution.

Question

z–3≥1
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 \( z - 3 \geq 1 \), follow these steps:

1. Isolate \( z \): \[ z - 3 \geq 1 \] Add 3 to both sides: \[ z \geq 1 + 3 \] \[ z \geq 4 \]

2. Graph the solution:

   • The solution \( z \geq 4 \) means that \( z \) can take any value greater than or equal to 4.
   • On a number line, plot a closed dot at 4, since the inequality includes equal to, and shade to the right (indicating all numbers greater than 4).

3. Changing an endpoint from closed to open:

   • You must choose to make one endpoint open. However, for the inequality \( z \geq 4 \), the endpoint (4) will remain closed since values larger than 4 are included.
   • If we consider an alternative or a hypothetical range such as \( z > 4 \), it would make sense to change it to an open endpoint. In that case, you would plot an open dot at 4 and shade to the right.

4. Deleting the middle segment (if applicable):

   • However, in this case, since the solution involves values greater than or equal to 4, there is no segment to delete.

Final Graph:

• If we keep \( z \geq 4 \): Closed dot at 4 and shading to the right.
• If we hypothetically consider \( z > 4 \): Open dot at 4 and shading to the right.

You can visualize this via a number line:

<---|---|---|---|---|---|--> (Numbers)
    2   3   4   5   6

For z >= 4: Closed dot at 4 and shade to the right
For z > 4: Open dot at 4 and shade to the right

Choose one of these visualizations according to the context you wish to consider.