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To solve the inequality \(3y - 2x \leq 1\) for \(y\) in terms of \(x\), follow these steps:

1. **Isolate the term with \(y\)**:
   \[
   3y \leq 2x + 1
   \]

2. **Divide all terms by 3** to solve for \(y\):
   \[
   y \leq \frac{2x + 1}{3}
   \]

So, the correct answer is **B: \( y \leq \frac{2x + 1}{3} \)**.

Would you like more details or have any questions? Here are some related questions:

1. How do you solve inequalities involving two variables?
2. What is the significance of the inequality sign when solving for \( y \)?
3. How do you graph an inequality after solving it in terms of \( y \)?
4. What are the steps to check the solution of an inequality?
5. How would the answer change if the inequality was \( 3y - 2x \geq 1 \)?

**Tip:** Always carefully check the direction of the inequality sign when dividing by a negative number, as it will reverse the inequality direction!

Select the choice that represents the two-variable inequality after it has been solved for y in terms of x: 3y - 2x ≤ 1.

Learn how to solve the two-variable linear inequality 3y - 2x ≤ 1 by isolating y in terms of x. This solution covers key algebraic concepts, including solving inequalities and dividing by constants, suitable for students in Grades 8-10.

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