Asked by evergreen
or
Solve the inequality and graph the solution.
p+2
2
≤
–
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.
Answers
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Answered by
GPT-4o mini
To solve the inequality
\[
\frac{p + 2}{2} \leq -1,
\]
we first start by multiplying both sides by 2 to eliminate the fraction:
\[
p + 2 \leq -2.
\]
Next, we isolate \(p\) by subtracting 2 from both sides:
\[
p \leq -2 - 2,
\]
which simplifies to:
\[
p \leq -4.
\]
Now, let's represent \(p \leq -4\) on a number line.
1. **Identifying Endpoints**: The endpoint in this case is \(-4\).
2. **Closed/Open Endpoint**: Since the inequality is less than or equal to (\(\leq\)), we will use a closed dot at \(-4\) to indicate that this point is included in the solution set.
3. **Graphing the solution**: The solution includes all numbers less than or equal to \(-4\).
### Number Line Graph:
- Mark \(-4\) with a closed dot.
- Shade to the left of \(-4\) to indicate all numbers less than \(-4\).
Here's a textual representation:
```
<---●============================>
-4
```
In summary, the solution to the inequality is \(p \leq -4\), represented on the number line with a closed dot at \(-4\) and shading to the left.
\[
\frac{p + 2}{2} \leq -1,
\]
we first start by multiplying both sides by 2 to eliminate the fraction:
\[
p + 2 \leq -2.
\]
Next, we isolate \(p\) by subtracting 2 from both sides:
\[
p \leq -2 - 2,
\]
which simplifies to:
\[
p \leq -4.
\]
Now, let's represent \(p \leq -4\) on a number line.
1. **Identifying Endpoints**: The endpoint in this case is \(-4\).
2. **Closed/Open Endpoint**: Since the inequality is less than or equal to (\(\leq\)), we will use a closed dot at \(-4\) to indicate that this point is included in the solution set.
3. **Graphing the solution**: The solution includes all numbers less than or equal to \(-4\).
### Number Line Graph:
- Mark \(-4\) with a closed dot.
- Shade to the left of \(-4\) to indicate all numbers less than \(-4\).
Here's a textual representation:
```
<---●============================>
-4
```
In summary, the solution to the inequality is \(p \leq -4\), represented on the number line with a closed dot at \(-4\) and shading to the left.
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