Write `(-5,9]` in set builder form .

Answer

To write the interval `(-5, 9]` in set builder form, we follow these steps:

### Step 1: Identify the interval
The interval `(-5, 9]` indicates that the values start just above -5 (not including -5) and go up to and including 9.

### Step 2: Define the variable
Let’s denote the variable as \( x \).

### Step 3: Determine the conditions for \( x \)
Since \( x \) must be greater than -5 and less than or equal to 9, we can express this mathematically as:
- \( x > -5 \) (because -5 is not included)
- \( x \leq 9 \) (because 9 is included)

### Step 4: Write in set builder notation
Using the conditions identified, we can write the set in set builder notation as follows:
\[ A = \{ x \mid x \in \mathbb{R}, -5 < x \leq 9 \} \]
Here, \( \mathbb{R} \) denotes the set of all real numbers.

### Final Answer
Thus, the set builder form of the interval `(-5, 9]` is:
\[ A = \{ x \mid x \in \mathbb{R}, -5 < x \leq 9 \} \]

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