An algebra problem by Ardhiana Yahya Ramadhan

$\begin{cases} b + 2x = a & ...(1) \\ 3a + 2x = b & ...(2) \\ a+b = c & ...(3) \end{cases}$

$\begin{aligned} (1)+(2): \quad 3a+b+4x & = a+b \\ 2a + 4x & = 0 \\ \implies a & = - 2x \end{aligned}$

$\begin{aligned} (1): \quad b+2x & = -2x \\ \implies b & = - 4x \end{aligned}$

$\begin{aligned} (3): \quad a+b & = c \\ \implies c & = - 6x \end{aligned}$

Therefore, $a+b+c = -2x-4x-6x = -12x$ and its maximum value is thus $\boxed{-12}$ , when $x = 1$ , the smallest.

a- b = 2x = -3a+b.So a=-2x, and b=2a. Because a+b=c, we get c=3a.Then a+b+c =6a.Put a=-2 to get max value. So max.(a+b+c) = -12