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We are given the inequality:

\[
x - \frac{y}{2} \leq -2x + 1
\]

We need to solve for \( y \) in terms of \( x \).

### Step-by-step solution:

1. **Move \( x \) to the other side:**
   \[
   - \frac{y}{2} \leq -2x + 1 - x
   \]
   Simplifying the right-hand side:
   \[
   - \frac{y}{2} \leq -3x + 1
   \]

2. **Multiply both sides by \(-2\)** to eliminate the fraction and solve for \( y \):
   \[
   y \geq (-2)(-3x + 1)
   \]
   Distribute the \(-2\) on the right-hand side:
   \[
   y \geq 6x - 2
   \]

### Final inequality:
\[
y \geq 6x - 2
\]

This corresponds to option **C**.

Let me know if you would like further details or have any questions!

Here are 5 related questions you might explore:
1. How do you solve inequalities involving fractions?
2. What happens when multiplying inequalities by negative numbers?
3. How would the solution change if the inequality were strict (using \( < \) or \( > \))?
4. What are the key differences between solving equations and inequalities?
5. How can graphing help in visualizing inequality solutions?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number.

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

Learn how to solve the two-variable inequality x - y/2 ≤ -2x + 1 for y in terms of x. This solution demonstrates the step-by-step process, including moving variables and multiplying by a negative. Suitable for Grades 7-9 students studying inequalities.

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