To solve the inequality \( z - 3 \geq 1 \), follow these steps:
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Isolate \( z \): \[ z - 3 \geq 1 \] Add 3 to both sides: \[ z \geq 1 + 3 \] \[ z \geq 4 \]
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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).
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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.
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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.