Write the following statements in symbols :
the integers less than 3 and greater than -2

Answer

To write the statement "the integers less than 3 and greater than -2" in symbols, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variable**: Let \( x \) represent an integer.
- **Hint**: Choose a variable to represent the integers you are discussing.

2. **Identify the Conditions**: The statement specifies two conditions:
- \( x \) must be less than 3.
- \( x \) must be greater than -2.

3. **Write the Inequalities**: Based on the conditions:
- The condition "less than 3" can be written as \( x < 3 \).
- The condition "greater than -2" can be written as \( x > -2 \).

4. **Combine the Inequalities**: Since both conditions must be true at the same time, we can combine them:
- This can be expressed as \( -2 < x < 3 \).

5. **Include the Set of Integers**: To specify that \( x \) is an integer, we can write:
- \( x \in \mathbb{Z} \), where \( \mathbb{Z} \) represents the set of all integers.

6. **Final Expression**: Therefore, the complete expression in symbols is:
- \( x \in \mathbb{Z} \) and \( -2 < x < 3 \).

### Final Answer:
\[ x \in \mathbb{Z} \quad \text{and} \quad -2 < x < 3 \]