Originally Posted by
Ackbeet Hmm. Start out as follows:
$\displaystyle a+x=b$ Given.
There is a vector $\displaystyle 0$ such that for any vector $\displaystyle y$, we have $\displaystyle y+0=0+y=y$.
Since $\displaystyle a$ is a vector, there is another vector, call it $\displaystyle -a$, such that $\displaystyle a+(-1)=0$. We add this vector $\displaystyle -a$ to both sides: $\displaystyle -a+(a+x)=-a+b$.
Since addition is associative and commutative, we may rewrite as follows:
$\displaystyle (-a+a)+x=b-a$. Can you finish?