If ` xinZ^(+)`, find the solution set of each of the following inequations : `7xlt17`

Answer

To solve the inequality \( 7x < 17 \) given that \( x \) belongs to the set of positive integers, we will follow these steps:

### Step 1: Write the inequality
We start with the inequality:
\[ 7x < 17 \]

### Step 2: Divide both sides by 7
To isolate \( x \), we divide both sides of the inequality by 7:
\[ x < \frac{17}{7} \]

### Step 3: Calculate \( \frac{17}{7} \)
Now, we need to calculate \( \frac{17}{7} \):
\[ \frac{17}{7} \approx 2.42857 \]

### Step 4: Identify the positive integers less than \( 2.42857 \)
Since \( x \) must be a positive integer, we look for positive integers that are less than \( 2.42857 \). The positive integers are:
1, 2, 3, 4, ...

The integers less than \( 2.42857 \) are:
- 1
- 2

### Step 5: Write the solution set
Thus, the solution set for the inequality \( 7x < 17 \) where \( x \) is a positive integer is:
\[ \{ 1, 2 \} \]

### Summary of the solution
The final answer is:
\[ x \in \{ 1, 2 \} \]

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