To solve the inequality:

$-11 + 8x \geq 13$

Step 1: Isolate the term with $x$

Add 11 to both sides of the inequality:

$8x \geq 13 + 11$

$8x \geq 24$

Step 2: Solve for $x$

Now, divide both sides by 8:

$x \geq \frac{24}{8}$

$x \geq 3$

So, the solution is $x \geq 3$.

Step 3: Graph the solution

The solution $x \geq 3$ means that $x$ includes all values greater than or equal to 3. On a number line, we represent this as a solid circle at $x = 3$ and shade the line to the right of 3 to indicate all numbers greater than or equal to 3.

Would you like me to graph this for you?

If you have further questions or need more details, feel free to ask. Here are a few related questions:

1. What happens if the inequality was $8x < 24$?
2. How would you solve a similar inequality involving fractions?
3. How do you check your solution for inequalities?
4. Can you graph this inequality on a different scale?
5. What is the solution if the inequality had been $8x \leq 24$?

Tip: Always remember to flip the inequality sign when dividing or multiplying both sides by a negative number.