And or or Compound Inequality

SUMMARY

A pair of vertical lines represents an absolute value

For absolute value inequalities:

'<' tells you it will be an AND compound inequality

'>' tells you it will be an OR compound inequality

Open circles represent '<' or '>' symbols

Notice that the inequality symbol points in the same direction as the arrow in our graph

NOTES

It is important to recognize what type of compound inequality an absolute value inequality will breakdown into

For absolute value inequalities, '<' means you will have an AND compound inequality

For absolute value inequalities, '>' means you will have an OR compound inequality

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

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'<' means you will have an AND compound inequality

'>' means you will have an OR compound inequality

The first absolute value inequality is '|x-5|<3'



The '<' symbol means LESS THAN

Since we're dealing with an absolute value, we have two options for inequalities

The absolute value inequality is '|x-5|<3'

Taking away the absolute value symbols, we get 'x-5<3'


Taking away the absolute value symbols, we get 'x-5<3'

Flipping the inequality symbol and changing the sign on the right, we get 'x-5>-3'

Our compound inequality is 'x-5<3 AND x-5>-3'

The second absolute value inequality is '|x-5|>3'





The '>' symbol means GREATER THAN

Since we're dealing with an absolute value, we have two options for inequalities

The absolute value inequality is '|x-5|>3'

Taking away the absolute value symbols, we get 'x-5>3'

Flipping the inequality symbol and changing the sign on the right, we get 'x-5<-3'

Our compound inequality is 'x-5>3 OR x-5<-3'

The absolute value inequalities are '|x-5|<3' and '|x-5|>3'

Our compound inequalities are 'x-5<3 AND x-5>-3' and 'x-5>3 OR x-5<-3'

The absolute value inequalities are '|x-5|<3' and '|x-5|>3'

Our compound inequalities are 'x-5<3 AND x-5>-3' and 'x-5>3 OR x-5<-3'

Our first compound inequality is 'x-5<3 AND x-5>-3'





Remember that we use open circles for inequalities with '<' or '>'

Notice the arrow we're drawing points in the same direction as the inequality symbol













So our graph and absolute value inequality agree!



Our graph and absolute value inequality agree!

Our second compound inequality is 'x-5>3 AND x-5<-3'
















"The absolute value of x minus 5 will always be GREATER THAN 3" can be written as '|x-5|>3'





The '<' symbol means LESS THAN

The '>' symbol means GREATER THAN



Documents

And or or Compound Inequality