To solve the problem, we start with the equation \( b \times 8 + 25 = 500 \), where \( b \) represents the number of beads Niel started with.
To isolate \( b \), we will perform the following operations:
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Subtraction: First, we subtract 25 from both sides to get the total number of beads used for the necklaces: \[ b \times 8 = 500 - 25 \]
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Division: Next, we divide both sides by 8 to find out how many beads were used in each necklace: \[ b = \frac{(500 - 25)}{8} \]
Thus, the necessary operations to solve for \( b \) are subtraction and division.
The correct response is: subtraction and division