What should be added to 8 (3x 4y) to obtain (18 x - 18 y) ?

Options

A. `6 x -14 y`
B. ` 14 y + 6x`
C. ` 14 y - 6 x `
D. 6xy

Answer

To solve the problem, we need to find what should be added to \( 8(3x - 4y) \) to obtain \( 18x - 18y \).

### Step-by-step Solution:

1. **Start with the expression**: We have \( 8(3x - 4y) \).

\[ 8(3x - 4y) = 8 \cdot 3x - 8 \cdot 4y = 24x - 32y \]

2. **Set up the equation**: We want to find \( t \) such that:

\[ 24x - 32y + t = 18x - 18y \]

3. **Rearranging the equation**: To isolate \( t \), we can rearrange the equation:

\[ t = (18x - 18y) - (24x - 32y) \]

4. **Distributing the negative sign**: Now, distribute the negative sign:

\[ t = 18x - 18y - 24x + 32y \]

5. **Combine like terms**: Now, combine the \( x \) and \( y \) terms:

\[ t = (18x - 24x) + (-18y + 32y) \]
\[ t = -6x + 14y \]

6. **Final expression for \( t \)**: Thus, we find that:

\[ t = 14y - 6x \]

### Conclusion:
To obtain \( 18x - 18y \) from \( 8(3x - 4y) \), you need to add \( 14y - 6x \).