For which integers $a$, $b$, and $c$, does $a - b + c = a - (b - c)$? Justify your answer.



Choose the correct answer below.

AThe equation is true for all integers.

$\begin{aligned}

a-b & +c \\

& =a+-b+c \\

& =a+-(b+-c) \\

& =a-(b-c)

\end{aligned}$

BThe equation is true for all integers $a$ and $c$ and $b \geq 0$.

$\begin{aligned}

a-b & +c \\

& =a+-b+c \\

& =a+{ }^{-}\left(b+{ }^{-} c\right), \text { for } b \geq 0 \\

& =a-(b-c)

\end{aligned}$

CThe equation is true for all integers $a$ and all integers $b$ and $c$ such that $b-c \geq 0$.

$\begin{aligned}

a-b & +c \\

& =a+-b+c \\

& =a+{ }^{-}\left(b+{ }^{-} c\right) \\

& =a-(b-c), \text { for } b-c \geq 0

\end{aligned}$

DThe equation is true for all integers $a$ and $b$ and $c \geq 0$.

$\begin{aligned}

a- & b+c \\

& =a+-b+c \\

& =a+{ }^{-}\left(b+{ }^{-} c\right), \text { for } c \geq 0 \\

& =a-(b-c)

\end{aligned}$