Solve : `7 gt 3x -8 , x in N`

Answer

To solve the inequality \( 7 > 3x - 8 \) where \( x \) belongs to the natural numbers (N), we can follow these steps:

### Step 1: Rewrite the Inequality
Start with the original inequality:
\[ 7 > 3x - 8 \]

### Step 2: Add 8 to Both Sides
To isolate the term with \( x \), add 8 to both sides of the inequality:
\[ 7 + 8 > 3x \]
This simplifies to:
\[ 15 > 3x \]

### Step 3: Rewrite the Inequality
We can rewrite the inequality as:
\[ 3x < 15 \]

### Step 4: Divide Both Sides by 3
Next, divide both sides of the inequality by 3 to solve for \( x \):
\[ x < \frac{15}{3} \]
This simplifies to:
\[ x < 5 \]

### Step 5: Identify Natural Number Solutions
Since \( x \) must be a natural number (N), we consider the natural numbers less than 5. The natural numbers are 1, 2, 3, 4. Therefore, the possible values for \( x \) are:
\[ x = 1, 2, 3, 4 \]

### Final Solution
The solution set for \( x \) in natural numbers is:
\[ \{1, 2, 3, 4\} \]

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