Algebra · Foundation · 11 min
Absolute value
Absolute value measures distance along a number line.
WHAT HAPPENS IF…With h=1 and r=2, is x=-1 included?
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Connect the picture to the idea∣x−h∣≤r⟺h−r≤x≤h+r(r≥0)The distance from x to h is x−h on the right and h−x on the left. Requiring either distance to be at most r gives a closed interval centered at h.
A detail that matters|x−h| is distance from h, not necessarily distance from zero.