3x+3 ≤6 and -2y>-10 convert to interval notation

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.

3x + 3 ≤ 6 and -2y > -10 convert to interval notation

Learn how to solve the inequalities 3x + 3 ≤ 6 and -2y > -10 and convert them into interval notation. This detailed step-by-step solution explains key algebraic concepts and how to handle inequality reversal when dividing by a negative number. Ideal for Grades 9-10 students.

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