If a and b are positive integers, then the solution of the equation `ax = b` will always be a

Options

A. positive number
B. negative number
C. 1
D. 0

Answer

To solve the equation \( ax = b \) for \( x \), we will follow these steps:

### Step 1: Write down the equation
We start with the equation:
\[ ax = b \]

### Step 2: Isolate \( x \)
To isolate \( x \), we need to divide both sides of the equation by \( a \) (since \( a \) is a positive integer and not equal to zero):
\[ x = \frac{b}{a} \]

### Step 3: Analyze the values of \( a \) and \( b \)
Given that both \( a \) and \( b \) are positive integers, we know that \( b \) is greater than zero and \( a \) is also greater than zero.

### Step 4: Determine the sign of \( x \)
Since both \( b \) and \( a \) are positive integers, the division \( \frac{b}{a} \) will also yield a positive result. Therefore, \( x \) will be a positive integer.

### Conclusion
Thus, we can conclude that the solution \( x \) of the equation \( ax = b \) will always be a positive integer.