Use interval notation to represent each set of numbers.

1. -15 < x < 0

A: (-15, 0)?

Rewrite each set in the indicate notation.

2. (Negative infinity, 3] or (5, 11]; words.

A: ?

1. -15 < x < 0 can be written in interval notation as (-15, 0).

To understand why, let's break it down step by step:

- The inequality -15 < x states that x is greater than -15, but not equal to -15. In interval notation, we use a parenthesis "(" for exclusive endpoints, meaning -15 is not included in the set. So, we start with (-15, ...).

- The inequality x < 0 states that x is less than 0. In interval notation, we use a parenthesis ")" for exclusive endpoints, meaning 0 is not included in the set. So, we end with (-15, 0).

Therefore, the interval notation for -15 < x < 0 is (-15, 0).

2. (Negative infinity, 3] or (5, 11]; words can be written in interval notation as (-∞, 3] U (5, 11).

To understand why, let's analyze each part:

- The notation (Negative infinity, 3] represents all numbers less than 3, including 3. In interval notation, we use square brackets "]" for inclusive endpoints, meaning 3 is included in the set. Since it starts from negative infinity (-∞) and goes up to 3, we have (-∞, 3].

- The notation (5, 11] represents all numbers greater than 5 and less than or equal to 11. In interval notation, we use parenthesis "(" for exclusive endpoints, meaning 5 and 11 are not included in the set. Therefore, we have (5, 11].

Since we have two intervals given with the word "or," we use the union symbol "U" to combine them. Therefore, the interval notation for (Negative infinity, 3] or (5, 11]; words is (-∞, 3] U (5, 11).

1: correct

2: (∞,3]U(5,11]
all values less than or equal to 11, except those greater than 3 and less than or equal to 5.