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The inequality given is:

\[
x - 3y \leq 4x
\]

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

### Steps:
1. Subtract \( x \) from both sides of the inequality:
   \[
   -3y \leq 4x - x
   \]
   Simplify:
   \[
   -3y \leq 3x
   \]

2. Divide both sides by \( -3 \) to solve for \( y \), and remember to reverse the inequality sign because we're dividing by a negative number:
   \[
   y \geq \frac{3x}{-3}
   \]
   Simplify:
   \[
   y \geq -x
   \]

Thus, the inequality solved for \( y \) in terms of \( x \) is:

\[
y \geq -x
\]

Would you like further details on solving inequalities or any other concepts? Here are 5 related questions to consider:

1. How do you solve inequalities involving absolute values?
2. What happens when you multiply or divide both sides of an inequality by a negative number?
3. How can you graph the inequality \( y \geq -x \) on a coordinate plane?
4. What are the differences between solving equalities and inequalities?
5. How can systems of inequalities be solved graphically?

**Tip:** When solving inequalities, always remember to reverse 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 - 3y ≤ 4x.

Learn how to solve the linear inequality x - 3y ≤ 4x for y in terms of x. This step-by-step guide covers key algebraic concepts, such as solving for a variable and reversing inequality signs. Suitable for students in Grades 8-10.

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