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Inequalities

# Inequalities - a> b and b> c then a> c Therefore if...

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Inequalities An  inequality  is a statement in which the relationships are not equal. Instead of using an equal sign  (=) as in an equation, these symbols are used: > (is greater than) and < (is less than) or   (is greater  than or equal to) and   (is less than or equal to).  Axioms and properties of inequalities For all real numbers  a, b,  and  c,  the following are some basic rules for using the inequality signs.  Trichotomy axiom:   a  >  b a  =  b , or  a  <  b These are the only possible relationships between two numbers. Either the first number is  greater than the second, the numbers are equal, or the first number is less than the second. Transitive axiom:  If  a  >
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Unformatted text preview: a > b , and b > c, then a > c. Therefore, if 3 > 2 and 2 > 1, then 3 > 1. If a < b and b < c, then a < c . Therefore, if 4 < 5 and 5 < 6, then 4 < 6. • Addition property: • If a > b , then a + c > b + c . • If a > b , then a – c > b – c . • If a < b , then a + c < b + c . • If a < b , then a – c < b – c . Adding or subtracting the same amount from each side of an inequality keeps the direction of the inequality the same. Example: If 3 > 2, then 3 + 1 > 2 + 1 (4 > 3) If 12 < 15, then 12 – 4 < 15 – 4 (8 < 11)...
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