Solve `-3+x lt 2, x in N`.

Answer

To solve the inequality \(-3 + x < 2\) where \(x\) belongs to the natural numbers, we will follow these steps:

### Step 1: Write the inequality
We start with the given inequality:
\[ -3 + x < 2 \]

### Step 2: Isolate \(x\)
To isolate \(x\), we will add 3 to both sides of the inequality:
\[ -3 + x + 3 < 2 + 3 \]
This simplifies to:
\[ x < 5 \]

### Step 3: Determine the natural number solutions
Since \(x\) must be a natural number (i.e., \(x \in \mathbb{N}\)), we need to find the natural numbers that are less than 5. The natural numbers start from 1 and include all positive integers.

The natural numbers less than 5 are:
\[ 1, 2, 3, 4 \]

### Conclusion
Thus, the solutions to the inequality \(-3 + x < 2\) where \(x\) is a natural number are:
\[ x = 1, 2, 3, 4 \]

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