What should be subtracted from `5y - 13x - 8a` to obtain `11x - 16y + 7a`?

Options

A. `24x - 21 y + a`
B. `6x + 21y + 15a`
C. `21y - 5x - a`
D. `21y - 24x - 15a`

Answer

To find out what should be subtracted from \(5y - 13x - 8a\) to obtain \(11x - 16y + 7a\), we can set up the equation as follows:

1. **Set up the equation**: We need to find an expression \(A\) such that:
\[ 5y - 13x - 8a - A = 11x - 16y + 7a \]

2. **Rearranging the equation**: To find \(A\), we can rearrange the equation:
\[ A = 5y - 13x - 8a - (11x - 16y + 7a) \]

3. **Distributing the negative sign**: Now, distribute the negative sign across the terms in the parentheses:
\[ A = 5y - 13x - 8a - 11x + 16y - 7a \]

4. **Combining like terms**: Now, combine the like terms:
- For \(y\): \(5y + 16y = 21y\)
- For \(x\): \(-13x - 11x = -24x\)
- For \(a\): \(-8a - 7a = -15a\)

Putting it all together:
\[ A = 21y - 24x - 15a \]

5. **Final answer**: Therefore, the expression that should be subtracted from \(5y - 13x - 8a\) to obtain \(11x - 16y + 7a\) is:
\[ 21y - 24x - 15a \]