Solve the inequality and graph the solution.

Question

r–6
2
>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

\[ \frac{r - 6}{2} > 1, \]

we can start by multiplying both sides by 2 (since 2 is positive, the direction of the inequality does not change):

\[ r - 6 > 2. \]

Next, we isolate \( r \) by adding 6 to both sides:

\[ r > 8. \]

This means that the solution to the inequality is any value of \( r \) that is greater than 8.

Graphing the Solution

1. Plot the point at \( r = 8 \).
2. Since the inequality is strict (greater than), we use an open circle at 8 to indicate that 8 is not included in the solution.
3. Shade to the right of 8, indicating that all values greater than 8 are part of the solution.

Summary of the Graph:

• Open circle at \( r = 8 \) (not included in the solution).
• Arrow extending to the right indicating all values greater than 8 are included.

The graph can be represented as follows:

<--------(8)===================>

In this representation:

• (8) indicates an open circle at 8 (not included).
• ==================> indicates the region where \( r > 8 \).