Grade 9 · Solve a two-direction distance condition · 123 of 750
Solve a two-direction distance condition · practice 13
Solve |x − (1)| = 7.5. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
Solve |x − (1)| = 7.5.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Absolute value here measures distance from the center on the number line.
Work through the reasoning
Step 1
Translate the givens
The center is 1 and the required distance is 7.5, which is nonnegative.
Step 2
Calculate with the model
Move 7.5 units left or right: x = 1 − 7.5 = -6.5 or x = 1 + 7.5 = 8.5.
Step 3
Check and interpret
Both substitutions have absolute difference 7.5. The two distinct positions are equally far from the center.
The answer
x = -6.5 or x = 8.5.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
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.
The mathematical idea
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. Starting quantities: Center c = 1; Required distance d = 7.5.
|x−c|=d → x=c−d or x=c+d
03 · Reflect and transfer
Explain what changes and why.
What would happen if the requested distance were negative?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.