Solve the inequality and graph the solution.

Question

–
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 \( u < -4 \).