Question
Use the grouping symbols to interpret the following equation the equation represents a product ? (1 point ) z/8 = (3(z + 4))/2 Which expression in (3(z + 4))/2; z/x; 3(z + 4) 02
Answers
GPT-4o mini
To interpret the equation \( \frac{z}{8} = \frac{3(z + 4)}{2} \), we need to examine the expressions involved, particularly focusing on the expression \( \frac{3(z + 4)}{2} \).
The right side of the equation, \( \frac{3(z + 4)}{2} \), can be understood as follows:
1. Here, \( z + 4 \) is first calculated, representing the sum of \( z \) and 4.
2. After that, this sum is multiplied by 3.
3. Finally, the result is divided by 2.
Thus, \( \frac{3(z + 4)}{2} \) represents a product because it includes multiplication (specifically, 3 multiplied by the expression \( z + 4 \)) before dividing by 2.
However, if we are specifically identifying which expressions represent a product, we can compare them:
- \( 3(z + 4) \) explicitly indicates a multiplication of 3 by \( (z + 4) \).
Therefore, among the options you've presented:
- \( \frac{3(z + 4)}{2} \): Represents not just a product, but is also a quotient.
- \( \frac{z}{x} \): This represents a quotient.
- \( 3(z + 4) \): This explicitly represents a product.
Thus, the expression that represents a product is **\( 3(z + 4) \)**.
The right side of the equation, \( \frac{3(z + 4)}{2} \), can be understood as follows:
1. Here, \( z + 4 \) is first calculated, representing the sum of \( z \) and 4.
2. After that, this sum is multiplied by 3.
3. Finally, the result is divided by 2.
Thus, \( \frac{3(z + 4)}{2} \) represents a product because it includes multiplication (specifically, 3 multiplied by the expression \( z + 4 \)) before dividing by 2.
However, if we are specifically identifying which expressions represent a product, we can compare them:
- \( 3(z + 4) \) explicitly indicates a multiplication of 3 by \( (z + 4) \).
Therefore, among the options you've presented:
- \( \frac{3(z + 4)}{2} \): Represents not just a product, but is also a quotient.
- \( \frac{z}{x} \): This represents a quotient.
- \( 3(z + 4) \): This explicitly represents a product.
Thus, the expression that represents a product is **\( 3(z + 4) \)**.