Grade 9 · Distance equations
Route marker: Solve a two-direction distance condition
Route marker investigation: solve a two-direction distance condition. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.
Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
Understand what you are seeing
The idea behind the motion.
Absolute value measures a nonnegative distance from a center on the number line. A positive fixed distance gives two positions, one on each side. At distance zero the two positions coincide, leaving one solution rather than two distinct answers. This investigation begins with center c = 4; required distance d = 5. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
|x−c|=d → x=c−d or x=c+d
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Mark the center c and confirm that the required distance d is nonnegative.
- STEP 2
Follow the changing model
Playback moves two points equally far in opposite directions from the center.
- STEP 3
Check and explain the relationship
Substitute both final positions into the absolute-value equation; if d=0, recognize that both expressions name the same point.
Your turn to explain
Make a prediction. Test your reasoning.
Route marker: Solve |x−(4)|=5.
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
x=-1 or x=9. Both lie 5 units from 4.
Work through a full lesson
Connect the animation to a worked example and practice questions.