For all real numbers a, b, and c: if a = b, then a + c = b + c. This is the ____ ____ of Equality.

Solution:

Given:

a, b, c are real numbers

The equivalence property of equality for addition says if a = b, then a + c = b + c.

By using substitution,

a + c = b + c

Using the substitution a = b, we get

a + c = a + c

Example: let a = 3 = b and c = 9

a + b = b + c

Using the value of a, b and c

3 + 9 = 3 + 9

12 = 12

Thus, if a = b, then a + c = b + c.

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For all real numbers a, b, and c: if a = b, then a + c = b + c. This is the ____ ____ of Equality.

Summary:

This is the Equivalence Property of Equality.