Which statement describes the Substitution Property?

• A. A quantity may not be substituted in any expression.
• B. A quantity may be substituted for any expression without regard to equality.
• C. A quantity may be substituted only if the numbers are different.
• D. A quantity may be substituted for its equal in any expression.

Answer: (D)

Substitution in algebra means that equal quantities can replace each other in any expression without changing the value. If two quantities are equal, you can swap one for the other inside an expression. For example, if a = 5, then in an expression like 2a + 7 you can substitute a with 5 to get 2(5) + 7 = 17. More generally, if a = b, you can replace a by b (or b by a) in any expression and keep the value the same. The statement that a quantity may be substituted for its equal in any expression captures this idea exactly.

This works only when the quantities are equal; it’s not valid to substitute without equality, nor to require the numbers to be different, nor to prohibit substitution when equality holds.