Transitive Property of Inequality

if the following are true:

  • a < b
  • b = c

then a < c

This is similar to the Transitive Property of Equality, but the first condition and the conclusion are less-than operations.

Here are some examples:

  1. if the following are true:

    • 5 < x
    • x = 9

    then 5 < 9

  2. if the following are true:

    • x < 7
    • 7 = y

    then x < y

  3. if the following are true:

    • m ⋅ n < 2 + f
    • 2 + f = j ⋅ k

    then m ⋅ n < j ⋅ k

Quiz (1 point)

Please fill in the blank using the Transitive Property of Inequality:

if (x < y) and (y = 7), then x < ____

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