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Solve the inequality and graph the solution. – (n–3)>1 Plot the endpoints. Select an endpoint to change it from closed to open....Asked by evergreen
Solve the inequality and graph the solution.
20>5z
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.
20>5z
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
Answered by
GPT-4o mini
To solve the inequality \( 20 > 5z \), we first manipulate the inequality to isolate \( z \).
1. Divide both sides by 5:
\[
\frac{20}{5} > z
\]
This simplifies to:
\[
4 > z
\]
or equivalently,
\[
z < 4
\]
Now, we can determine the solution in interval notation:
- The solution set is \( (-\infty, 4) \).
### Graphing the Solution
To graph this inequality:
1. **Endpoints**: The endpoint is \( 4 \).
2. Since \( z < 4 \), we use an open circle at \( 4 \) (because \( 4 \) is not included in the solution).
3. We draw a line (or ray) extending to the left towards negative infinity.
### Final Representation
- The graph should show an open circle at \( 4 \) with a line extending leftward:
**Graph Representation**:
\[
\text{(Circle at 4)} \quad \text{(Line to left)} \quad \text{(Arrow indicating it goes to } -\infty\text{)}
\]
Thus, the solution to the inequality \( 20 > 5z \) is \( z < 4 \) represented as \( (-\infty, 4) \) on the number line.
1. Divide both sides by 5:
\[
\frac{20}{5} > z
\]
This simplifies to:
\[
4 > z
\]
or equivalently,
\[
z < 4
\]
Now, we can determine the solution in interval notation:
- The solution set is \( (-\infty, 4) \).
### Graphing the Solution
To graph this inequality:
1. **Endpoints**: The endpoint is \( 4 \).
2. Since \( z < 4 \), we use an open circle at \( 4 \) (because \( 4 \) is not included in the solution).
3. We draw a line (or ray) extending to the left towards negative infinity.
### Final Representation
- The graph should show an open circle at \( 4 \) with a line extending leftward:
**Graph Representation**:
\[
\text{(Circle at 4)} \quad \text{(Line to left)} \quad \text{(Arrow indicating it goes to } -\infty\text{)}
\]
Thus, the solution to the inequality \( 20 > 5z \) is \( z < 4 \) represented as \( (-\infty, 4) \) on the number line.
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