When are the expressions 3x + 12 and 3(x + 4) equivalent? Explain how you know. A. The expressions are always equivalent. By the Distributive Property, 3(x + 4) = 3x + 12. This means that, no matter what value is substituted for x, 3x + 12 = 3(x + 4).
B. The expressions are equivalent when x = 5. Substituting 5 for x results in a value of 27 for each of the expressions. However, substituting any other value for x gives different values for the two expressions.
C. The expressions are equivalent when x = 0 and when x = 5. Substituting either of these values for x results in equal values for each of the expressions. However, substituting any other value for x gives different values for the two expressions.
D. The expressions are never equivalent. Adding 12 to 3x will always give a different result than adding 4 to x and then multiplying the result by 3.