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We are given the inequality:

\[
7y + 2 \leq -3y - 8
\]

Let's solve this step by step:

### Step 1: Move all terms with \( y \) to one side
Add \( 3y \) to both sides to combine like terms:

\[
7y + 3y + 2 \leq -3y + 3y - 8
\]

\[
10y + 2 \leq -8
\]

### Step 2: Move constant terms to the other side
Subtract \( 2 \) from both sides:

\[
10y + 2 - 2 \leq -8 - 2
\]

\[
10y \leq -10
\]

### Step 3: Solve for \( y \)
Divide both sides by \( 10 \):

\[
y \leq \frac{-10}{10}
\]

\[
y \leq -1
\]

### Final Answer:
From the options given, the correct choice is **B. \( y \leq -1 \)**.

Would you like more details or have any questions?

Here are 5 related questions to further explore inequalities:
1. How do you solve inequalities with fractions?
2. What happens when you multiply or divide both sides of an inequality by a negative number?
3. How can you graph the solution of an inequality on a number line?
4. What are the differences between solving an equation and an inequality?
5. How would the inequality change if the signs were reversed?

**Tip:** Always remember that when you multiply or divide both sides of an inequality by a negative number, the inequality symbol flips!

Solve the inequality 7y + 2 ≤ -3y - 8 and select your answer from the choices given.

Learn how to solve the linear inequality 7y + 2 ≤ -3y - 8 with a detailed step-by-step solution. This problem explores key algebra concepts and is suitable for students in Grades 7-9. Find the correct solution and answer from the provided choices.

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