There are several different ways we can solve this inequality graphically.

1. > f:= x -> abs(x-3);
   

   > 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.

2. > plot(f(x)-g(x),x=-10..10);
   

   In this case, we see for which x the graph of the difference |x - 3| - |x + 4| is above the x-axis.

3. > h:=x->abs(x-3)>abs(x+4);
   

   > 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);