The inequality given is:

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

To solve for \(r\), follow these steps:

### Step 1: Eliminate the denominator by multiplying both sides by \(-4\).
- When multiplying both sides of an inequality by a negative number, the inequality sign must be reversed:

\[
3 + r \geq 6 \times -4
\]

\[
3 + r \geq -24
\]

### Step 2: Isolate \(r\) by subtracting 3 from both sides:

\[
r \geq -24 - 3
\]

\[
r \geq -27
\]

Thus, the solution is \( r \geq -27 \).

### Final Answer:
\[
r \geq -27
\]

Would you like more details on any part of this solution?

Here are 5 related questions for practice:
1. Solve: \(\frac{5 + x}{-3} \leq 7\)
2. Solve: \(\frac{2 + y}{4} \geq -5\)
3. Solve: \(\frac{r - 8}{-5} > 3\)
4. Solve: \(4r + 6 \leq 18\)
5. Solve: \(r - 3 > 10\)

**Tip:** When multiplying or dividing inequalities by a negative number, always remember to flip the inequality sign!

Learn how to solve the inequality (3 + r) / -4 <= 6. This step-by-step solution covers algebraic concepts such as manipulating inequalities and reversing inequality signs when multiplying by negative numbers. Suitable for students in Grades 7-9.

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