Question

Solve the inequality and graph the solution.
7(k–1)–9>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

Let's solve the inequality step by step:

1. Start with the inequality:
\[
7(k - 1) - 9 > 5
\]

2. Distribute the 7:
\[
7k - 7 - 9 > 5
\]
Simplifying gives:
\[
7k - 16 > 5
\]

3. Add 16 to both sides to isolate the term with \( k \):
\[
7k > 21
\]

4. Divide both sides by 7:
\[
k > 3
\]

Now we have the solution \( k > 3 \).

### Graphing the Solution

- The solution involves \( k \) values that are greater than 3.
- The endpoint at \( k = 3 \) should be highlighted as an open endpoint since our inequality is strictly greater than (>): it does not include 3.

Here is a description of how to represent the solution on a number line:

1. Draw a number line.
2. Mark the point 3 on the number line.
3. Use an open circle at 3 to indicate that 3 is not included in the solution.
4. Shade the region to the right of 3 to represent all the numbers greater than 3.

Thus, you have the graph that shows all \( k \) values greater than 3, with an open circle at 3. The final solution is:
\[
\boxed{k > 3}
\]