[Math] If $a | b – 2c$ and $a | 2b + 3c$ then $a | b$ and $a | c$. true or false proof? Discrete maths

Question

If $a | b-2c$ then $b-2c = ak$ and if $a|2b+3c$ then $2b+3c = al$ .
So I tried doing a direct proof and I get $c = \frac{al-2ak}{7}$ where $a$ and $k$ are integers. $b = \frac{2al+3ak}{7}$ . The question also states $a,b$ and $c$ are integers .
I can't figure out if it's true or false help plz.

Answer 1

Your computations say that it's wrong. Try $a=7$, $b=5$ and $c=-1$.