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Inequality Rules

Inequality Rules

Algebra rules for manipulating inequalities are listed below.

 

Definitions: 1. a<b means a is smaller than b. 2. a≤b means a is smaller than or equal to b. 3. a>b means a is larger than b....

Operations: 1. Addition: if a<b then a+c<b+c; for a≤b, a>b, a≥b. 2. Subtraction: if a<b then a-c<b-c; for a≤b, a>b, a≥b.
Rules 3–6 for inequalities: multiplication/division by positive/negative c, showing direction changes when c<0, with examples...

Transitive Property of Inequalities

If a < b and b < c , then a < c.
If a ≤ b and b ≤ c , then a ≤ c.
If a > b and b > c , then a > c.
If a ≥ b and b ≥ c , then a ≥ c.

 

See also

Equation rules, trichotomy, equivalence properties of equality