Rewrite the set I by listing its elements. Make sure to use the appropriate set notation.
I={y |y  is an integer and <−5<y−3}

The given set \( I = \{ y \mid y \text{ is an integer and } -5 < y - 3 \} \) can be rewritten by solving the inequality for \( y \).

Starting with the inequality:
\[
-5 < y - 3
\]
Add 3 to both sides:
\[
-5 + 3 < y \quad \Rightarrow \quad -2 < y
\]

This means \( y \) must be an integer greater than \( -2 \). Therefore, the set \( I \) includes all integers greater than \( -2 \), which can be written as:
\[
I = \{ -1, 0, 1, 2, 3, 4, \dots \}
\]

This is the set of all integers starting from \( -1 \) and increasing without bound.

Would you like any further details or clarification?

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Here are five related questions:
1. How do you solve inequalities involving absolute values?
2. How would the set change if \( y - 3 \leq -5 \)?
3. What happens if you add a condition like \( y < 10 \)?
4. Can you list the elements of the set \( \{ y \mid -2 \leq y \leq 5 \} \)?
5. How do you represent an infinite set on a number line?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number!

Rewrite the set I by listing its elements. Make sure to use the appropriate set notation. I = {y | y is an integer and -5 < y - 3}

Learn how to solve the inequality -5 < y - 3 and rewrite the set I in appropriate set notation. This problem covers key mathematical concepts like inequalities and integer sets, perfect for students in Grades 6-8.

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