Solve the inequality and graph the solution.

Question

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.