To solve the inequality \( 3 + \frac{r}{-4} \leq 6 \), follow these steps:

### Step 1: Isolate the term involving \( r \)
Start by subtracting 3 from both sides of the inequality:

\[
3 + \frac{r}{-4} - 3 \leq 6 - 3
\]

This simplifies to:

\[
\frac{r}{-4} \leq 3
\]

### Step 2: Eliminate the fraction
Multiply both sides of the inequality by \(-4\) to eliminate the fraction. Remember that multiplying by a negative number reverses the inequality sign:

\[
r \geq 3 \times (-4)
\]

\[
r \geq -12
\]

### Final Solution:
The solution to the inequality is:

\[
r \geq -12
\]

Would you like further details or have any questions about the solution? Here are 5 related questions you might consider:

1. How do we solve inequalities involving absolute values?
2. What happens when you multiply or divide both sides of an inequality by a negative number?
3. How do we graph the solution to an inequality on a number line?
4. Can inequalities have multiple solutions?
5. How do inequalities change when involving quadratic expressions?

**Tip:** When multiplying or dividing by a negative number in an inequality, always remember to reverse the inequality sign!

Learn how to solve the inequality 3 + r / -4 ≤ 6 with this detailed, step-by-step guide. This problem focuses on algebraic concepts, including inequalities and handling negative numbers. Suitable for students in Grades 8-10.

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