Find the solution set of `2x-7lt8,x inN`. Represent the solution set on the number line.

Answer

To solve the inequality \(2x - 7 < 8\) for \(x\) in the set of natural numbers (\(N\)), we will follow these steps:

### Step 1: Rewrite the inequality
Start with the given inequality:
\[ 2x - 7 < 8 \]

### Step 2: Isolate the term with \(x\)
To isolate \(2x\), add \(7\) to both sides of the inequality:
\[ 2x - 7 + 7 < 8 + 7 \]
This simplifies to:
\[ 2x < 15 \]

### Step 3: Solve for \(x\)
Next, divide both sides by \(2\) to solve for \(x\):
\[ x < \frac{15}{2} \]
Calculating \(\frac{15}{2}\) gives:
\[ x < 7.5 \]

### Step 4: Identify natural numbers
Since \(x\) must be a natural number, we consider the natural numbers less than \(7.5\). The natural numbers are \(1, 2, 3, 4, 5, 6, 7\).

### Step 5: Write the solution set
Thus, the solution set is:
\[ \{1, 2, 3, 4, 5, 6, 7\} \]

### Step 6: Represent the solution set on a number line
To represent this solution set on a number line, we will mark the points \(1, 2, 3, 4, 5, 6, 7\) with dots, indicating that these are the natural numbers included in our solution set.

### Final Answer
The solution set is \(\{1, 2, 3, 4, 5, 6, 7\}\).

---