Solve the inequality and graph the solution.

Question

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.