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What's a Compound Inequality?

Definition: Compound Inequality

Summary

  1. A compound inequality combines two simple inequalities with an "AND" or "OR"
  2. 'x>7' is a simple inequality, connected to the simple inequality 'x<15' by an 'AND'
  3. 'x<-5' is a simple inequality, connected to the simple inequality 'x>3' by an 'OR'
  4. The set-builder notation for 'x>7 AND x<15' looks like:
  5. '{x | 7<x<15}'
  6. The set-builder notation for 'x<-5 OR x>3' looks like:
  7. '{x | x<-5 OR x>3}'

Notes

    1. So there are two types of compound inequalities: AND or OR
    1. So there are two types of compound inequalities: AND or OR
    1. There are two types of compound inequalities: AND or OR
    1. An AND compound inequality will have an "AND" between two simple inequalities
    1. An AND compound inequality will have an "AND" between two simple inequalities
    2. So 'x is GREATER THAN 7' and 'x is LESS THAN 15' are two simple inequalities, connected by an 'AND'
    3. The '>' symbol means GREATER THAN
    4. The '<' symbol means LESS THAN
    1. This is an AND compound inequality
    2. 'x is GREATER THAN 7' and 'x is LESS THAN 15' are two simple inequalities, connected by an 'AND'
    3. The '>' symbol means GREATER THAN
    4. The '<' symbol means LESS THAN
    1. An OR compound inequality will have an "OR" between two simple inequalities
    1. An OR compound inequality will have an "OR" between two simple inequalities
    2. So 'x is GREATER LESS -5' and 'x is GREATER THAN 3' are two simple inequalities, connected by an 'OR'
    3. The '<' symbol means LESS THAN
    4. The '>' symbol means GREATER THAN
    1. This is an OR compound inequality
    2. 'x is GREATER LESS -5' and 'x is GREATER THAN 3' are two simple inequalities, connected by an 'OR'
    3. The '<' symbol means LESS THAN
    4. The '>' symbol means GREATER THAN
    1. Remember, there are two types of compound inequalities: AND or OR
    1. Our AND compound inequality was: 'x>7 AND x<15'
    2. Our OR compound inequality was: 'x<-5 AND x>3'
    3. The '>' symbol means GREATER THAN
    4. The '<' symbol means LESS THAN
    1. Our AND compound inequality was: 'x>7 AND x<15'
    2. Opening up our set just means to write a left curly brace, '{'
    3. 'x' is a variable representing the numbers in our set
    4. The vertical line, '|', means we're about to define what numbers 'x' represents in the set
    5. Since we're flip-flopping our inequality, we need to flip the inequality symbol, too!
    6. So 'x>7' is the same as '7<x'
    7. Since we already have the 'x' written, we can just write the '<15' part
    8. Close a set with a right curly brace, '}'
    1. Our set-builder notation for 'x>7 AND x<15' looks like:
    2. '{x | 7<x<15}'
    1. Our OR compound inequality was: 'x<-5 AND x>3'
    2. Opening up our set just means to write a left curly brace, '{'
    3. 'x' is a variable representing the numbers in our set
    4. The vertical line, '|', means we're about to define what numbers 'x' represents in the set
    5. We can only get the simplified set-builder notation with AND compound inequalities
    6. So we just rewrite 'x<-5 OR x>3' after the '{x |'
    7. Close a set with a right curly brace, '}'
    1. Our set-builder notation for 'x>7 AND x<15' looks like:
    2. '{x | 7<x<15}'
    3. Our set-builder notation for 'x<-5 OR x>3' looks like:
    4. '{x | x<-5 OR x>3}'