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The inequality you provided is:

\[
-5 \leq \frac{k}{4} - 9
\]

To solve this inequality for \(k\), let's go step by step.

### Step 1: Add 9 to both sides
\[
-5 + 9 \leq \frac{k}{4}
\]
This simplifies to:
\[
4 \leq \frac{k}{4}
\]

### Step 2: Multiply both sides by 4
\[
4 \times 4 \leq k
\]
This simplifies to:
\[
16 \leq k
\]

Thus, the solution is:
\[
k \geq 16
\]

Would you like more details on any part of the process? Here are five related questions you might find interesting:

1. How do you solve inequalities involving variables and fractions?
2. What happens if you multiply or divide both sides of an inequality by a negative number?
3. Can you explain how to graph the solution \( k \geq 16 \)?
4. What is the difference between solving equations and solving inequalities?
5. How do you check if a solution to an inequality is correct?

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

Learn how to solve the linear inequality -5 ≤ k/4 - 9 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequality manipulation and variable isolation. Suitable for students in Grades 6-8.

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