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Absolute Value Inequality Calculator

Online absolute value inequality solver: |ax+b|≤c gives an interval, ≥c gives two parts, with a number line.

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|X|≤c ⇔ −c≤X≤c; |X|≥c two parts
−32
a≠0
Inside is ax+b
Usually c≥0
Pick sign

📖 Tutorial | Absolute Inequality

1. Definition
|X|≤c (c≥0) ⇔ −c≤X≤c; |X|≥c ⇔ X≤−c or X≥c; |X| is the distance from zero.
2. Formula & Notation
X=ax+bInside the bars
3. Properties & Laws
  • |X|≤c gives an interval;
  • |X|≥c gives two parts;
  • c<0: none/all;
  • |X|=c gives ±c.
4. Steps
  1. Enter a (≠0), b, c and a sign;
  2. Click "Solve";
  3. Or click "Load Example".
5. Worked Examples
Example: |2x+1|≤5 → −3≤x≤2.
6. Common Pitfalls
Ensure c≥0;
Dividing by negative a flips the sign (auto);
≥ has two parts.

❓ FAQ | Absolute Inequality

≤c?
Interval.
≥c?
Two parts.
c<0?
None/all.
Geometry?
Distance.
=c?
±c.
Negative a?
Flip.
Endpoints?
Included for ≤/≥.