Question

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.

Answer 1

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.