Question

Solve the inequality.
1. 3s + 6 less than or equal to -5(s+2)
2. -5r + 6 less than or equal to -5(r+2)

Answer 1

Let's solve each inequality step by step.

### 1. Solve the inequality \( 3s + 6 \leq -5(s + 2) \).

**Step 1: Expand the right side.**
\[
-5(s + 2) = -5s - 10
\]
So the inequality becomes:
\[
3s + 6 \leq -5s - 10
\]

**Step 2: Add \( 5s \) to both sides to consolidate the \( s \) terms.**
\[
3s + 5s + 6 \leq -10
\]
\[
8s + 6 \leq -10
\]

**Step 3: Subtract 6 from both sides.**
\[
8s \leq -10 - 6
\]
\[
8s \leq -16
\]

**Step 4: Divide both sides by 8.**
\[
s \leq -2
\]

The solution to the inequality is:
\[
s \leq -2
\]

---

### 2. Solve the inequality \( -5r + 6 \leq -5(r + 2) \).

**Step 1: Expand the right side.**
\[
-5(r + 2) = -5r - 10
\]
So the inequality becomes:
\[
-5r + 6 \leq -5r - 10
\]

**Step 2: Add \( 5r \) to both sides.**
\[
-5r + 5r + 6 \leq -10
\]
\[
6 \leq -10
\]

This statement \( 6 \leq -10 \) is false.

The solution to this inequality is:
\[
\text{No solution}
\]

### Summary of Solutions:
1. \( s \leq -2 \)
2. No solution for the second inequality.