Solve the inequality and graph the solution.

Question

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: \[ \boxed{k > 3} \]