Solve the inequality and graph the solution.

Question

k–13
–
11
≤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

\[ \frac{k - 13}{11} \leq 1, \]

we will first isolate \( k \).

Step 1: Multiply both sides by 11 to eliminate the fraction (note that since 11 is positive, the inequality direction does not change):

\[ k - 13 \leq 11. \]

Step 2: Add 13 to both sides to solve for \( k \):

\[ k \leq 11 + 13, \] \[ k \leq 24. \]

The solution set is

\[ k \in (-\infty, 24]. \]

Graphing the Solution

To graph the solution \( k \leq 24 \):

1. Draw a number line.
2. Mark the endpoint at 24.
3. Since \( k \leq 24 \) includes the point 24, plot it as a closed point (●).
4. Shade the line to the left of 24, indicating that all values less than and including 24 are part of the solution.

Final Graph

• The graph will have a closed circle at 24 and a shaded region extending to negative infinity to the left.

Thus, the final solution indicates that \( k \) can take any value up to and including 24.

If required to choose an endpoint to change from closed to open, we could select 24, but this would not be appropriate for our original inequality since it includes the endpoint. For this valid inequality, the endpoint remains closed.

In summary, our solution is:

\[ k \leq 24 \]

Graph:

• Closed dot at 24.
• Shade left towards \(-\infty\).