There are several different ways we can solve this inequality graphically.
> g:= x -> abs(x+4);
> plot({f(x),g(x)},x=-10...10);
We now see that the red graph which is the graph of f is above the green graph which is the graph of g for x < -1/2.
In this case, we see for which x the graph of the difference |x - 3| - |x + 4| is above the x-axis.
> plot(h(x),x=-10..10,thickness=2);
In this case, we are plotting the truth function which has the value 1 when |x - 3| > |x + 4| and the value 0 otherwise.
> solve(abs(x-3)>abs(x+4),x);