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← Inequalities Checking - College Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

  1. >> Here are our answers. You've learned that inequalities have ranges of values
  2. that are solutions to them. So that means that if a number falls in this range,
  3. we can use it in the inequality to make a true statement. Some of these may be a
  4. bit confusing though. For example, 3 is less than or equal to 7. On a number
  5. line, if we're curious about all of the numbers that are less than or equal to
  6. 7, we would shade in all the numbers to the left of 7 on the number line. And
  7. then draw a square bracket to include 7 in that range. We can see that 3
  8. definitely falls in this region. It is not equal to 7, but it is less than 7.
  9. And it only needs to fit one of the criteria implied by this symbol. It either
  10. needs to be less than 7, or it needs to be equal to 7. Similarly, the statement
  11. 8 is greater than or equal to 1 plus 7 is also true. When simplified, this of
  12. course gives us the inequality 8 is greater than or equal to 8. And you might at
  13. first think, oh my gosh, 8 is not greater than 8. However it only needs to be
  14. greater than or equal to 8. It's equal to 8 so that's enough to satisfy this
  15. inequality. We can see the difference here then, between this symbol, the
  16. greater than or equal to, which implies inclusion of 8, versus the just greater
  17. than sign. This statement is true. Whereas this statement is not, because 8 is
  18. greater than 1 plus 7, only allows for the greater than criterion, not the equal
  19. to one. 1 plus 7 no longer fits the bill.