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What Are Some Words We Use To Write Inequalities?

Definition: Words That Indicate Different Types of Inequalities

Summary

  1. Since we already know some simple inequalities, we're looking at more difficult ones
  2. A compound inequality is a combination of simple inequalities
  3. 'x' and 'y' are variables representing numbers here
  4. Direction does not matter for an absolute value inequality, only the number of units between the values does
  5. 'Curr. - Fut.' represents the difference between John's current and future weight

Notes

    1. Since we already know some simple inequalities, we're looking at more difficult ones
    1. We're going to translate word phrases into inequalities
    1. This is what a compound inequality is, a combination of simple inequalities!
    1. We're translating a word phrase into a compound inequality
    2. 'x' and 'y' are variables representing numbers here
    3. Notice that 'MORE THAN' translates to a '>' symbol and 'LESS THAN' translates to a '<' symbol
    1. 'GREATER THAN', or '>', is one simple inequality
    2. 'LESS THAN', or '<', is another simple inequality
    1. Two simple inequalities combined forms a compound inequality
    1. We're translating a word phrase into a compound inequality
    1. We're translating a word phrase into a compound inequality
    2. 'x' and 'y' are variables representing numbers here
    3. Notice that 'AT LEAST' translates to a '≥' symbol and 'LESS THAN OR EQUAL TO' translates to a '≤'
    1. Two simple inequalities combined forms a compound inequality
    2. 'GREATER THAN OR EQUAL TO', or '≥', is one simple inequality
    3. 'LESS THAN OR EQUAL TO', or '≤', is another simple inequality
    1. Two simple inequalities combined forms a compound inequality
    1. We're translating a word phrase into a compound inequality
    1. We're translating a word phrase into a compound inequality
    2. 'x' and 'y' are variables representing numbers here
    3. Notice that 'BETWEEN' translates to '<' on the left of 'Value' and '>' on the right!
    1. We're translating a word phrase into a compound inequality
    1. We're translating a word phrase into a compound inequality
    2. Notice that 'LESS THAN' translates to a '<' symbol
    3. Notice that 'John's Height' is 'GREATER THAN OR EQUAL TO 5ft', so '5ft' is 'LESS THAN OR EQUAL TO' his height!
    1. We're going to translate word phrases into absolute value inequalities
    1. Direction does not matter for an absolute value inequality, only the number of units between the values does
    1. We're translating a word phrase into an absolute value inequality
    1. We're translating a word phrase into an absolute value inequality
    2. 'x' is a variable representing a number here
    3. Notice that 'NO MORE THAN' translates to a '≤' symbol
    1. This is what absolute values are all about
    1. 'overall difference' is really just the absolute value!
    1. We're translating a word phrase into an absolute value inequality
    1. We're translating a word phrase into an absolute value inequality
    2. 'y' is a variable representing a number here
    3. 'change between two numbers' is really just the absolute value!
    4. Notice that 'GREATER THAN' translates to a '>' symbol
    1. This is what absolute values are all about
    1. 'overall change' is really just the absolute value!
    1. We're translating a word phrase into an absolute value inequality
    1. We're translating a word phrase into an absolute value inequality
    2. 'x' is a variable representing a number here
    3. 'Range' is really just the absolute value!
    4. Notice that 'WITHIN' translates to a '<', or LESS THAN symbol, between 'Range' and 'x'
    1. 'number of units between values' is really just the absolute value of the difference between two numbers
    1. We're translating a word phrase into an absolute value inequality
    1. We're translating a word phrase into an absolute value inequality
    2. 'Current Weight - Future Weight' represents the change in John's weight
    3. The absolute value bars show that the change can be negative or positive
    4. Notice that 'MUST NOT CHANGE MORE THAN' translates to a '≤' symbol