To solve the inequality
\[ \frac{m - 1}{5} > 1 \]
we can start by isolating \(m\). Here are the steps:
-
Multiply both sides by 5 (since 5 is positive, the direction of the inequality doesn't change):
\[ m - 1 > 5 \]
-
Add 1 to both sides:
\[ m > 6 \]
So the solution to the inequality is
\[ m > 6 \]
Graphing the Solution
- Plotting the Endpoint: Since the inequality is \(m > 6\), we will plot the endpoint \(6\) on a number line.
- Open Circle: We make this endpoint an open circle because \(m = 6\) is not included in the solution (the inequality is strict).
- 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.