Question

Solve the inequality and graph the solution.
m–1
5
>1
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

\[
\frac{m - 1}{5} > 1
\]

we can start by isolating \(m\). Here are the steps:

1. **Multiply both sides by 5** (since 5 is positive, the direction of the inequality doesn't change):

\[
m - 1 > 5
\]

2. **Add 1 to both sides**:

\[
m > 6
\]

So the solution to the inequality is

\[
m > 6
\]

### Graphing the Solution

1. **Plotting the Endpoint**: Since the inequality is \(m > 6\), we will plot the endpoint \(6\) on a number line.
2. **Open Circle**: We make this endpoint an open circle because \(m = 6\) is not included in the solution (the inequality is strict).
3. **Arrow/Ray**: Draw an arrow to the right from the open circle indicating that all values greater than \(6\) are included in the solution.

Thus, the graph would look like this:

```
<---o======================>
6
```
Here, the open circle at \(6\) represents that \(6\) is not included in the solution set, and the arrow indicates that the solution continues to positive infinity.