Question

Solve the inequality and graph the solution.
–
1>
u–1
5
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 \( -1 > \frac{u - 1}{5} \), we start by eliminating the fraction. First, we can multiply both sides by 5 to isolate \( u - 1 \):

\[
-5 > u - 1
\]

Next, we can rearrange the inequality to solve for \( u \):

\[
-5 + 1 > u
\]
\[
-4 > u
\]

This is the same as saying:

\[
u < -4
\]

### Solution Set:
The solution set consists of all values of \( u \) that are less than -4.

### Graphing the Solution:
To graph \( u < -4 \):
- We will place an open circle at -4 (indicating that -4 is not included in the solution set).
- We will draw a ray extending to the left from -4, representing all values less than -4.

Here's how you do it step-by-step:
1. Plot an open circle at -4 on a number line.
2. Shade all the area to the left of -4 to represent all numbers less than -4.

### Summary of the Graph:
- **Endpoint**: The point at -4 will be an **open circle**.
- **Direction**: A ray extending to the left to indicate all values less than -4.

This represents all \( u \) such that \( u < -4 \).