Problem 11
Question
Sketch the region that corresponds to the given inequalities, say whether the region is bounded or unbounded, and find the coordinates of all corner points (if any). $$ x \geq-5 $$
Step-by-Step Solution
Verified Answer
The region corresponding to the inequality \(x \geq -5\) is the area to the right of the vertical line at \(x = -5\), including the line itself. This region is unbounded, with no corner points.
1Step 1: Graphing the inequality
To graph the inequality \(x \geq -5\), plot a vertical line at \(x = -5\). Since the inequality is greater than or equal to \(-5\), the region that satisfies the inequality would be the area to the right of this vertical line, which includes the line itself.
2Step 2: Identifying the properties of the region
In this case, our region extends infinitely to the right of the vertical line at \(x = -5\). This makes our region unbounded, meaning it doesn't have a finite maximum or minimum value.
3Step 3: Identify any corner points
Since the region is unbounded, there are no corner points as the region stretches infinitely in various directions (up, down, and right) from the line \(x = -5\).
To summarize, the region that corresponds to the given inequality is the area to the right of the vertical line at \(x = -5\), including the line itself. The region is unbounded, and there are no corner points.
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Problem 11
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