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 Microcalc:
  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Graph y = F(x), press and .
  3. At the prompt, F(x) =, enter the function
    abs(x - 3)
  4. and use the bounds
    x0 = -10 x1 = 10
    y0 = -10 y1 = 10
  5. You will then see the graph of this function.
  6. Press the and, using the arrow keys, move to the menu item Superimpose and press .
  7. At the prompt F(x) = , enter
    abs(x + 4)
  8. You will then see the graphs of both functions on the screen.
  9. 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 first pressing .
  10. Using the arrow keys, move to Pinpoint, press and and you will see a cross on the screen.
  11. Use the right and left arrow keys to move the cross along one of the graphs. Use the up and down arrow keys to move between the two graphs. If you press the size in the jump of the x-coordinate will increase ten-fold. If you press the size in the jump of the x-coordinate will decrease ten-fold.
  12. As shown in the picture below, we 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 Microcalc:
  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Graph y = F(x), press and the spacebar
  3. and, at the prompt, F(x) =, enter the function
    abs(x - 3) - abs(x+4)
  4. and use the bounds
    x0 = -10 x1 = 10
    y0 = -10 y1 = 10
  5. You will then see the graph of this function. As in the previous "solution", you can now use Pinpoint to find the intersection of the graph with the x-axis.