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Use the grouping symbols to interpret the following equation: x/8 = 3(x + 4)/2. Which expression in the equation represents a product?

Option 1: 3(x + 4)/2
Option 2: 3 (x + 4)
Option 3: 2
Option 4: x/8

1 answer

To interpret the equation \( \frac{x}{8} = \frac{3(x + 4)}{2} \), we need to identify which expression represents a product.

Let's analyze the options:

  1. Option 1: \( \frac{3(x + 4)}{2} \) - This expression includes a fraction, where \( 3(x + 4) \) is in the numerator and represents a product of 3 and \( (x + 4) \).

  2. Option 2: \( 3(x + 4) \) - This is clearly a product of 3 and \( (x + 4) \).

  3. Option 3: 2 - This is just a number, and does not represent a product.

  4. Option 4: \( \frac{x}{8} \) - This expression includes a fraction, but it does not represent a product in the same sense as the others.

Based on this analysis, both Option 1 and Option 2 represent products. However, if you need to choose just one, the clearest answer would be:

Option 2: \( 3(x + 4) \), as it directly shows the product without any fraction involved.