www.VirtualNerd.com

What is an Identity Inequality?

What is an identity inequality?

Summary

  1. 2 is always less than 5 so 2 < 5 is an identity inequality
  2. '<' means 'less than'
  3. Try plugging values such as 5 or -5 into b2 ≥ 0 and you'll get true statements every time
  4. '≥' means 'greater than or equal to'
  5. Try plugging values such as 2 into the third example and you'll always get a true statement
  6. '>' means 'greater than'
  7. Try graphing an identity inequality on a number line -- all real numbers get filled in!

Notes

    1. Before we give the definition of an identity inequality, let's look at a few examples
    1. First, look at an example that only involves numbers
    2. '<' means 'less than'
    3. This inequality is obviously true because 2 is always less than 5
    1. Now let's look at an identity inequality that contains a variable on the left side
    2. 'b' is the variable here
    3. '≥' means 'greater than or equal to'
    4. This inequality is basically saying that whenever you square a number you get a number greater than or equal to 0
    5. To test this inequality, try plugging 5 in for 'b'
    6. 52 = 25
    7. Next, try plugging -5 in for 'b'
    8. (-5)2 = 25
    9. 25 is greater than 0, so this is an identity inequality!
    1. Finally, let's look at an identity inequality with variables on each side
    2. 'b' is the variable here
    3. '>' means 'greater than'
    4. To test this inequality, try plugging 2 in for 'b'
    5. 9•2-3 = 18-3 = 15
    6. 3(3(2)-3) = 3(6-3) = 3(3) = 9
    7. 15 is greater than 9, so this is true
    8. You can also simplify the inequality on both sides and get -3 > -9, which is a true statement!
    1. You just saw some examples -- let's go over the definition of an identity inequality
    2. We chose 5, -5, and 2 as our values for 'b', but we could have chosen any numbers
    3. Try graphing an identity inequality on a number line -- all real numbers get filled in!