turkey-yks 2020 Q6

turkey-yks · Other · yks-ayt Modulus function Solving equations involving modulus
For integers $x$ and $y$,
$$| x - 3 | + | 2 x + y | + | 2 x + y - 1 | = 1$$
the equality is satisfied. Accordingly, what is the sum of the values that $y$ can take?
A) $- 12$
B) $- 11$
C) $- 10$
D) $- 9$
E) $- 8$
For integers $x$ and $y$,

$$| x - 3 | + | 2 x + y | + | 2 x + y - 1 | = 1$$

the equality is satisfied. Accordingly, what is the sum of the values that $y$ can take?\\
A) $- 12$\\
B) $- 11$\\
C) $- 10$\\
D) $- 9$\\
E) $- 8$