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How Do You Figure Out if an Absolute Value Inequality is an AND or OR Compound Inequality?

Determine if these absolute value inequalities represent AND or OR compound inequalities: |x-5| < 3 and |x-5| > 3

Summary

  1. A pair of vertical lines represents an absolute value
  2. For absolute value inequalities:
  3. '<' tells you it will be an AND compound inequality
  4. '>' tells you it will be an OR compound inequality
  5. Open circles represent '<' or '>' symbols
  6. Notice that the inequality symbol points in the same direction as the arrow in our graph

Notes

    1. It is important to recognize what type of compound inequality an absolute value inequality will breakdown into
    1. For absolute value inequalities, '<' means you will have an AND compound inequality
    1. For absolute value inequalities, '>' means you will have an OR compound inequality
    1. For absolute value inequalities:
    2. '<' means you will have an AND compound inequality
    3. '>' means you will have an OR compound inequality
    1. The first absolute value inequality is '|x-5|<3'
    1. For absolute value inequalities:
    2. '<' means you will have an AND compound inequality
    3. The '<' symbol means LESS THAN
    1. Since we're dealing with an absolute value, we have two options for inequalities
    1. The absolute value inequality is '|x-5|<3'
    2. Taking away the absolute value symbols, we get 'x-5<3'
    1. The absolute value inequality is '|x-5|<3'
    2. Taking away the absolute value symbols, we get 'x-5<3'
    3. Flipping the inequality symbol and changing the sign on the right, we get 'x-5>-3'
    1. Our compound inequality is 'x-5<3 AND x-5>-3'
    1. The second absolute value inequality is '|x-5|>3'
    1. For absolute value inequalities:
    2. '>' means you will have an OR compound inequality
    3. The '>' symbol means GREATER THAN
    1. Since we're dealing with an absolute value, we have two options for inequalities
    2. The absolute value inequality is '|x-5|>3'
    3. Taking away the absolute value symbols, we get 'x-5>3'
    4. Flipping the inequality symbol and changing the sign on the right, we get 'x-5<-3'
    5. Our compound inequality is 'x-5>3 OR x-5<-3'
    1. The absolute value inequalities are '|x-5|<3' and '|x-5|>3'
    2. Our compound inequalities are 'x-5<3 AND x-5>-3' and 'x-5>3 OR x-5<-3'
    1. The absolute value inequalities are '|x-5|<3' and '|x-5|>3'
    2. Our compound inequalities are 'x-5<3 AND x-5>-3' and 'x-5>3 OR x-5<-3'
    1. Our first compound inequality is 'x-5<3 AND x-5>-3'
    1. Our first compound inequality is 'x-5<3 AND x-5>-3'
    1. Our first compound inequality is 'x-5<3 AND x-5>-3'
    2. Remember that we use open circles for inequalities with '<' or '>'
    3. Notice the arrow we're drawing points in the same direction as the inequality symbol
    1. Our first compound inequality is 'x-5<3 AND x-5>-3'
    2. Remember that we use open circles for inequalities with '<' or '>'
    3. Notice the arrow we're drawing points in the same direction as the inequality symbol
    1. Our first compound inequality is 'x-5<3 AND x-5>-3'
    2. Remember that we use open circles for inequalities with '<' or '>'
    3. Notice the arrow we're drawing points in the same direction as the inequality symbol
    1. Our first compound inequality is 'x-5<3 AND x-5>-3'
    2. The absolute value inequality is '|x-5|<3'
    1. Our first compound inequality is 'x-5<3 AND x-5>-3'
    2. The absolute value inequality is '|x-5|<3'
    1. Our first compound inequality is 'x-5<3 AND x-5>-3'
    2. The absolute value inequality is '|x-5|<3'
    3. So our graph and absolute value inequality agree!
    1. Our graph and absolute value inequality agree!
    1. Our second compound inequality is 'x-5>3 AND x-5<-3'
    1. Our second compound inequality is 'x-5>3 AND x-5<-3'
    2. Remember that we use open circles for inequalities with '<' or '>'
    3. Notice the arrow we're drawing points in the same direction as the inequality symbol
    1. Our second compound inequality is 'x-5>3 AND x-5<-3'
    2. Remember that we use open circles for inequalities with '<' or '>'
    3. Notice the arrow we're drawing points in the same direction as the inequality symbol
    1. Our second compound inequality is 'x-5>3 AND x-5<-3'
    2. Remember that we use open circles for inequalities with '<' or '>'
    3. Notice the arrow we're drawing points in the same direction as the inequality symbol
    1. Our second compound inequality is 'x-5>3 AND x-5<-3'
    2. Remember that we use open circles for inequalities with '<' or '>'
    3. Notice the arrow we're drawing points in the same direction as the inequality symbol
    4. Our graph and absolute value inequality agree!
    1. "The absolute value of x minus 5 will always be GREATER THAN 3" can be written as '|x-5|>3'
    2. Our graph and absolute value inequality agree!
    1. For absolute value inequalities:
    2. '<' means you will have an AND compound inequality
    3. '>' means you will have an OR compound inequality
    4. The '<' symbol means LESS THAN
    5. The '>' symbol means GREATER THAN