The integral solution set of the inequations `x gt -3` and `x lt 2` is _______.

Answer

To solve the inequations \( x > -3 \) and \( x < 2 \) and find the integral solution set, we can follow these steps:

### Step 1: Understand the Inequations
We have two inequations:
1. \( x > -3 \)
2. \( x < 2 \)

### Step 2: Represent the Inequations on a Number Line
On a number line, we can represent the points:
- The point \(-3\) will be an open circle (since \( x \) is greater than \(-3\), it does not include \(-3\)).
- The point \(2\) will also be an open circle (since \( x \) is less than \(2\), it does not include \(2\)).

### Step 3: Identify the Range of \( x \)
From the two inequations, we can combine them to find the range of \( x \):
- The solution set is \( -3 < x < 2 \).

### Step 4: Determine the Integral Solutions
Now we need to find the integral (whole number) solutions that lie within this range. The integers that satisfy \( -3 < x < 2 \) are:
- \(-2\)
- \(-1\)
- \(0\)
- \(1\)

### Step 5: List the Integral Solutions
Thus, the integral solution set is:
\[ \{-2, -1, 0, 1\} \]

### Final Answer
The integral solution set of the inequations \( x > -3 \) and \( x < 2 \) is \(\{-2, -1, 0, 1\}\).

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