To solve the inequality $8 + k \leq -3$:

Step 1: Isolate $k$

Subtract $8$ from both sides of the inequality:

$k \leq -3 - 8$

$k \leq -11$

Step 2: Graph the solution

The solution is $k \leq -11$. To graph this:

• Place a filled circle at $-11$ to indicate that $-11$ is included in the solution.
• Shade the number line to the left of $-11$ to represent all values less than or equal to $-11$.

If you'd like, I can clarify any part of this solution or create a graph for you!

Follow-up Questions:

1. How do you handle inequalities when dividing or multiplying by a negative number?
2. What does a filled versus an open circle on a number line indicate?
3. How would the solution change if the inequality were $8 + k < -3$?
4. Can you graph this inequality using interval notation?
5. How is solving inequalities different from solving equations?

Tip: Always check your solution by substituting the boundary value back into the original inequality.