To solve the inequality \(-16 \geq 8q\), let's first simplify it.
- Divide both sides by 8: \[ -2 \geq q \] This can be rewritten as: \[ q \leq -2 \]
Now, let's interpret this inequality:
- The solution means that \(q\) can take any value less than or equal to \(-2\).
Endpoint
The endpoint of the inequality is at \(q = -2\).
Graphing the Solution
To graph the solution on a number line:
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Plot the Endpoint -2: Since the inequality is \(q \leq -2\), we will use a closed dot (or circle) at \(-2\) to indicate that \(-2\) is included in the solution set.
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Shade to the Left: Since \(q \leq -2\) indicates all values less than \(-2\), we will shade to the left of \(-2\).
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Select an Endpoint to Change: If we were to change the endpoint from closed to open, we could choose to make \(-2\) an open circle. This would indicate that \(-2\) is not included in the solution set.
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Select the Middle Segment to Delete: Typically, in a less-than-or-equal inequality, you would not delete any middle segments, as the entire left ray should remain shaded. However, if you are specifically instructed to remove part of the line, you might remove the segment to the right of the open dot if you change it to an open circle.
Final Graph
The graph would look like this:
- A number line with an open circle at \(-2\).
- A shaded line extending to the left of \(-2\).
If you choose to keep \(-2\) as a closed point and only denote it visually as an open circle for the sake of exercise:
- Still shade to the left, but the actual inequality solution would retain \(-2\) as part of the solution.
Final notation would show as:
- \(q < -2\) if \(-2\) is open.
- \(q \leq -2\) if \(-2\) remains closed.
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