I have to proove that if $\{u,v,x\} \in V(G)$ where $G$ is connected and $uv \in E(G)$ then $$ |d_G(u,x) - d_G(x,v)| \leq 1 $$
I know that as the distance is a natural number then one is qreater or equal to the other, and also $d_G(u,v) = 1$ since $uv \in E(G)$ so for the triangle inequality we've got that $1 = d_G(u,v) \leq d_G(u,x) + d_G(x,v)$ but then...
HINT: on the one hand, $d_G(u,x) \le d_G(u,v) + d_G(v,x) = d_G(u,v)+d_G(x,v)$ [because $d_G(x,v)=d_G(v,x)$].
On the other hand, $d_G(x,v)=d_G(v,x) \le d_G(v,u) + d_G(u,x)$.
Now, the edge $uv$ is in $G$, so what is $d_G(v,u)=d_G(u,v)$ again?