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Let's solve the inequality step by step. We need to solve for \( y \) in terms of \( x \).

The inequality is:

\[
-6y < -3(y - 2x)
\]

### Step 1: Distribute the \(-3\) on the right side of the inequality.

\[
-6y < -3y + 6x
\]

### Step 2: Move all terms involving \( y \) to the left side of the inequality. Add \( 3y \) to both sides:

\[
-6y + 3y < 6x
\]

\[
-3y < 6x
\]

### Step 3: Solve for \( y \) by dividing both sides by \(-3\). Since we are dividing by a negative number, the direction of the inequality flips:

\[
y > -2x
\]

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

\[
y > -2x
\]

Would you like more details on any part of the solution?

### Relative Questions:
1. How do you flip the inequality sign when dividing by a negative number?
2. What happens if we have additional constants in the inequality?
3. How does solving for a variable differ between equalities and inequalities?
4. What are common mistakes when distributing in inequalities?
5. How would the solution change if there were more terms involving \( y \)?

### 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. -6y < -3(y - 2x)

Learn how to solve the linear inequality -6y < -3(y - 2x) for y in terms of x. This problem involves key algebraic concepts, including the distributive property and reversing inequalities when dividing by a negative number. Suitable for students in Grades 8-10.

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