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Name the property that justifies the following statement: If 2x + 4 = y and y = 3x - 6 then 2x + 4 = 3x - 6.

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Answer:

  transitive property of equality

Step-by-step explanation:

The transitive property of equality says ...

  if a = b and b = c, then a = c.

Here, we can use this form with ...

  a = 2x+4

  b = y

  c = 3x-6

__

We have ...

  a = b   ⇒   2x +4 = y

  b = c   ⇒   y = 3x -6

so, ...

  a = c   ⇒   2x +4 = 3x -6 . . . . transitive property of equality.

_____

On the other hand, ...

The substitution property of equality says ...

  if a = b, we can use b wherever 'a' is seen.

We can use this with ...

  a = y

  b = 3x -6

and do the substitution in the equation ...

  2x +4 = y

Replacing y with its equal, we get ...

  2x +4 = 'a'   ⇒   2x +4 = 'b'   ⇒   2x +4 = 3x -6 . . . . substitution property of equality

_____

Additional comment

These are two different ways to say that anything can be replaced by its equal.

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