Final answer:
The number that can replace the blank in the expression 24+21x=____ (8+7x) is 24+21x. It demonstrates the Distributive Property, which states that a(b+c) = ab + ac.
Step-by-step explanation:
The number that could replace the ___ in the problem 24+21x=____ (8+7x) is 24+21x, and the property it illustrates is the Distributive Property of multiplication over addition.
This property states that a(b+c) = ab + ac. In the given expression, if we distribute the 8 and 7x across the terms inside the parenthesis, we get 8+7x, which when multiplied by a common factor (which in this case could be 1 to maintain equality), gives us 24+21x.
Hence, by using the Distributive Property, we can simplify and evaluate expressions and equations effectively.