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To solve for \( y \) in the inequality:

\[
7x + 8y \leq 14x - 16
\]

### Step 1: Isolate the \( y \)-term on one side.
We start by subtracting \( 7x \) from both sides:

\[
8y \leq 14x - 16 - 7x
\]

Simplifying the right-hand side:

\[
8y \leq 7x - 16
\]

### Step 2: Solve for \( y \) by dividing both sides by 8:

\[
y \leq \frac{7x - 16}{8}
\]

We can split the fraction:

\[
y \leq \frac{7}{8}x - 2
\]

### Final Answer:

The inequality is \( y \leq \frac{7}{8}x - 2 \).

### Conclusion:
The correct answer is **Option A**: 
\[
y \leq \frac{7}{8}x - 2
\]

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Would you like further details or explanations on any part of the solution? Here are some related questions:

1. How do we solve linear inequalities involving two variables?
2. What are the differences between solving equations and inequalities?
3. How do we graph inequalities like \( y \leq \frac{7}{8}x - 2 \)?
4. What is the significance of dividing by a positive number in inequalities?
5. Can you explain how to handle inequalities when dividing by negative numbers?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number.

Learn how to solve the linear inequality 7x + 8y ≤ 14x - 16 with a detailed step-by-step solution. This problem covers key algebraic concepts, including isolating variables and dividing inequalities by constants. Suitable for students in Grades 9-10.

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