If `x inN`, find the solution set of each of the following inequations : `4xlt13`

Answer

To solve the inequality \( 4x < 13 \) where \( x \) belongs to the set of natural numbers \( \mathbb{N} \), we will follow these steps:

### Step 1: Start with the given inequality
We have the inequality:
\[ 4x < 13 \]

### Step 2: Divide both sides by 4
To isolate \( x \), we divide both sides of the inequality by 4. Remember that dividing by a positive number does not change the direction of the inequality.
\[ x < \frac{13}{4} \]

### Step 3: Simplify the fraction
Now, we simplify \( \frac{13}{4} \):
\[ \frac{13}{4} = 3.25 \]
So, we have:
\[ x < 3.25 \]

### Step 4: Identify the natural numbers less than 3.25
Since \( x \) must be a natural number (which includes positive integers: 1, 2, 3, ...), we need to find the natural numbers that are less than 3.25. The natural numbers less than 3.25 are:
- 1
- 2
- 3

### Step 5: Write the solution set
Thus, the solution set for the inequality \( 4x < 13 \) where \( x \) is a natural number is:
\[ \{ 1, 2, 3 \} \]

### Final Answer
The solution set is:
\[ \{ 1, 2, 3 \} \]

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