Write the following intervals in the set-builder form
(-7,0)

Answer

To write the interval (-7, 0) in set-builder form, we follow these steps:

### Step 1: Identify the interval
The given interval is (-7, 0). This means we are looking for all the numbers that are greater than -7 and less than 0.

### Step 2: Define the variable
Let’s denote the variable as \( x \). We want to express the values that \( x \) can take.

### Step 3: Establish the conditions
Since the interval is open on both ends (indicated by the parentheses), we know that:
- \( x \) must be greater than -7
- \( x \) must be less than 0

### Step 4: Write the conditions in mathematical form
We can express this as:
- \( -7 < x < 0 \)

### Step 5: Include the set notation
In set-builder notation, we also need to specify that \( x \) belongs to the set of real numbers. Thus, we write:
- \( x \in \mathbb{R} \)

### Step 6: Combine everything into set-builder form
Putting it all together, we write the set-builder form as:
\[ A = \{ x \in \mathbb{R} \mid -7 < x < 0 \} \]

### Final Answer
The set-builder form of the interval (-7, 0) is:
\[ A = \{ x \in \mathbb{R} \mid -7 < x < 0 \} \]

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