To convert the inequalities into interval notation, let's address each inequality separately:

First inequality:

$3x + 3 \leq 6$

1. Subtract 3 from both sides: $3x \leq 3$
2. Divide both sides by 3: $x \leq 1$ This corresponds to the interval: $(-\infty, 1]$

Second inequality:

$-2y > -10$

1. Divide both sides by -2. Remember, dividing by a negative number flips the inequality sign: $y < 5$ This corresponds to the interval: $(-\infty, 5)$

Final answer in interval notation:

For $x$: $(- \infty, 1]$ For $y$: $(- \infty, 5)$

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you handle inequalities when multiplying or dividing by a negative number?
2. Can you graph the solution of these inequalities on a number line?
3. What is the difference between strict inequalities and non-strict inequalities in interval notation?
4. How do we represent compound inequalities in interval notation?
5. How do the intervals change when solving systems of inequalities?

Tip: Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.