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

Options

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

Let \( m \) be the expression that we need to subtract. The equation can be written as:

\[ 5y - 13x - 8a - m = 11x - 16y + 7a \]

Now, we can rearrange this equation to solve for \( m \):

\[ m = 5y - 13x - 8a - (11x - 16y + 7a) \]

Next, we distribute the negative sign across the terms in the parentheses:

\[ m = 5y - 13x - 8a - 11x + 16y - 7a \]

Now, we combine like terms:

1. Combine the \( y \) terms:
\[ 5y + 16y = 21y \]

2. Combine the \( x \) terms:
\[ -13x - 11x = -24x \]

3. Combine the \( a \) terms:
\[ -8a - 7a = -15a \]

Putting it all together, we have:

\[ m = 21y - 24x - 15a \]

Thus, the expression that should be subtracted from \( 5y - 13x - 8a \) to obtain \( 11x - 16y + 7a \) is:

\[ 21y - 24x - 15a \]