Question

  

Multiple Select Question

Gopal is thinking of a number. He says that the sum of the number and 8, multiplied by 34, is equal to -12. Which equations can be used to find Gopal's number?

Choose all that apply.

A. 

3/4(x +8) = −12

B. 

3/4x +6 = −12

C. 

x + 6 = −12

D. 

3/4x +8 = −12

Answer 1

To determine which equations can represent Gopal's situation, we first need to translate the information given into a mathematical equation.

Gopal states that the sum of his number (let's call it \( x \)) and 8, multiplied by 34, is equal to -12. This can be expressed as:

\[
34(x + 8) = -12
\]

We can now look at the provided options:

A. \( \frac{3}{4}(x + 8) = -12 \)

This equation does not match the original since it has a factor of \( \frac{3}{4} \) instead of multiplying by 34. So this option does not apply.

B. \( \frac{3}{4}x + 6 = -12 \)

This equation also introduces different coefficients and does not correspond to the original equation. Therefore, this option does not apply.

C. \( x + 6 = -12 \)

This equation cannot be derived from the original statement. It is a basic linear equation that does not consider the multiplication by 34. So, this option does not apply.

D. \( \frac{3}{4}x + 8 = -12 \)

This option has a different structure and factors than what was provided and does not represent the original equation either. Hence, it does not apply.

None of the options A, B, C, or D properly reflect the equation derived from the problem statement \( 34(x + 8) = -12 \).

If we were to pick the correct form, it would be the equation I mentioned earlier. Thus, none of the provided options accurately represent Gopal's number situation.