Solve 5x<24 when `xinN`

Answer

To solve the inequality \( 5x < 24 \) where \( x \) belongs to the set of natural numbers, follow these steps:

### Step 1: Write the inequality
We start with the given inequality:
\[ 5x < 24 \]

### Step 2: Divide both sides by 5
To isolate \( x \), we divide both sides of the inequality by 5:
\[ x < \frac{24}{5} \]

### Step 3: Simplify the fraction
Now, we simplify \( \frac{24}{5} \):
\[ \frac{24}{5} = 4.8 \]
So, we have:
\[ x < 4.8 \]

### Step 4: Identify natural numbers less than 4.8
The natural numbers are defined as the positive integers: \( 1, 2, 3, 4, 5, \ldots \)
Since \( x \) must be a natural number and also less than 4.8, we list the natural numbers less than 4.8:
- The natural numbers are \( 1, 2, 3, 4 \)

### Step 5: Write the solution
Thus, the solution set for \( x \) in natural numbers is:
\[ x \in \{ 1, 2, 3, 4 \} \]

### Final Answer:
The natural numbers satisfying the inequality \( 5x < 24 \) are \( 1, 2, 3, \) and \( 4 \).

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