Geometric meaning of ∣x−a∣
The number ∣x−a∣ is the distance on the coordinate line from x to the fixed point a (no sign: always ≥0).
Standard rewrites follow:
• ∣x−a∣<b, b>0 ↔ the point x is closer than b to a ↔ a double linear inequality a−b<x<a+b.
• ∣x−a∣>b, b>0 ↔ two rays: x<a−b or x>a+b.
When b=0, ∣x−a∣≤0 gives the single point x=a.
When splitting cases do not forget b>0; if the right-hand side is negative you often get "no solution" or the whole line — check the context
Full content is available with a subscription.
Get full access to all courses on the platform for one year with a single payment.
▼
Unlike other platforms that charge per course, here you get everything for one price, and after one year of use there will be no automatic charge for the following year.