To solve the inequality $\frac{b}{2} + 8 \leq 10$, let's follow these steps:

Step 1: Subtract 8 from both sides

$\frac{b}{2} \leq 10 - 8$ $\frac{b}{2} \leq 2$

Step 2: Multiply both sides by 2 to isolate $b$

$b \leq 2 \times 2$ $b \leq 4$

Solution:

The solution to the inequality is $b \leq 4$. This means that $b$ can be any number less than or equal to 4.

Graphing the solution:

On a number line, we would place a closed circle at $b = 4$ and shade the line to the left, indicating that all values less than or equal to 4 are solutions.

---

Would you like further details or have any questions about this solution?

Here are five related questions for you:

1. How do you graph inequalities involving fractions?
2. How do you solve inequalities with variables on both sides?
3. What is the difference between strict and non-strict inequalities?
4. How do you handle multiplying or dividing by negative numbers in inequalities?
5. What is the significance of using a closed versus an open circle in graphing inequalities?

Tip: When solving inequalities, always remember that multiplying or dividing by a negative number reverses the inequality sign!