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.