Problem:
Graphically, solve the inequality:

|x - 3| > |x + 4|

Visualization #1:
Graph each of the functions

f(x) = |x - 3| and g(x) = |x + 4|

and determine the part of the graph of f which is above the graph of g:

Using MPP:
  1. Choose Item 1 - MPP (Mathematics Plotting Program from the initial menu and press .
  2. Enter the bounds
    Xmin : -10 Xmax : 10
    Ymin : -10 Ymax : 10 .
  3. At the prompt 1. y=f(x) ==>, enter the function
    abs(x + 4) .
  4. At the prompt 2. y=f(x) ==> , enter
    abs(x - 3)
  5. Press to display the graphs of the functions.
  6. The problem now is to convince the student that there is only one point of intersection of the two graphs and then to find this point. We can get an approximation to this point by using the Zoom-in feature of this program.
  7. Press ; you will then see a cross on the screen. Using the arrow keys move the cross close to the point of intersection and press .
  8. Again use the arrow keys to form a rectangle which contains the point of intersection and press . The part of graphs inside the rectangle are magnified.
  9. Repeat the previous two steps several times to see that the intersection of the two graphs is approximately x = -0.5.
Visualization #2:
Graph the function

f(x) = |x - 3| - |x + 4|

and determine the part of the graph of f which is above the x-axis:

Using MPP:
  1. Choose Item 1 - MPP (Mathematics Plotting Program from the initial menu and press .
  2. Enter the bounds
    Xmin : -10 Xmax : 10
    Ymin : -10 Ymax : 10 .
  3. At the prompt 1. y=f(x) ==>, enter the function
    abs(x-3)-abs(x + 4) .
  4. Press to display the graph of the function.
  5. As in the previous "solution", you can now use the Zoom-in feature of the program to find the intersection of the graph with the x-axis.