`{x : 3x-2 le 10 " and " x in N}`

Answer

To solve the problem `{x : 3x - 2 ≤ 10 " and " x in N}`, we will follow these steps:

### Step 1: Solve the inequality
We start with the inequality given in the problem:
\[ 3x - 2 \leq 10 \]

### Step 2: Isolate the term with x
To isolate the term with x, we add 2 to both sides of the inequality:
\[ 3x - 2 + 2 \leq 10 + 2 \]
This simplifies to:
\[ 3x \leq 12 \]

### Step 3: Divide by 3
Next, we divide both sides of the inequality by 3 to solve for x:
\[ \frac{3x}{3} \leq \frac{12}{3} \]
This simplifies to:
\[ x \leq 4 \]

### Step 4: Consider the natural numbers
Since we are given that \( x \) must be a natural number (N), we need to list the natural numbers that satisfy the inequality \( x \leq 4 \). The natural numbers are 1, 2, 3, 4, etc.

### Step 5: List the valid values
The natural numbers that are less than or equal to 4 are:
\[ 1, 2, 3, 4 \]

### Step 6: Write the final set
Thus, the set of values for \( x \) is:
\[ \{1, 2, 3, 4\} \]

### Final Answer
The final answer is:
\[ \{x : 3x - 2 \leq 10 \text{ and } x \in N\} = \{1, 2, 3, 4\} \]

---