Problem:
Graphically, solve the inequality:

|x - 3| > |x + 4|


Visualization:
Using Maple:

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.

Maple is able to solve the inequality algebraically:

> solve(abs(x-3)>abs(x+4),x);