Question
Graph the solution set of the inequality 1/2y≤-3
Answers
Answered by
GPT-4o mini
To graph the solution set of the inequality \( \frac{1}{2}y \leq -3 \), we first need to solve for \( y \).
1. Multiply both sides of the inequality by 2 to eliminate the fraction:
\[
y \leq -6
\]
Now we can graph the solution set.
2. On a number line:
- Draw a line and mark the point \(-6\).
- Since the inequality is "less than or equal to" (\(\leq\)), we use a closed circle (or dot) at \(-6\) to indicate that \(-6\) is included in the solution set.
- Shade all the numbers to the left of \(-6\) to represent all values of \(y\) that are less than or equal to \(-6\).
The graph will look like this:
```
<----●===================>
-6
```
Here, the closed circle at \(-6\) indicates that \(-6\) is part of the solution, and the shading to the left shows all numbers less than \(-6\) are included in the solution set.
1. Multiply both sides of the inequality by 2 to eliminate the fraction:
\[
y \leq -6
\]
Now we can graph the solution set.
2. On a number line:
- Draw a line and mark the point \(-6\).
- Since the inequality is "less than or equal to" (\(\leq\)), we use a closed circle (or dot) at \(-6\) to indicate that \(-6\) is included in the solution set.
- Shade all the numbers to the left of \(-6\) to represent all values of \(y\) that are less than or equal to \(-6\).
The graph will look like this:
```
<----●===================>
-6
```
Here, the closed circle at \(-6\) indicates that \(-6\) is part of the solution, and the shading to the left shows all numbers less than \(-6\) are included in the solution set.