Question

Expression A: 3x + 4

Expression B: 2+ 3x + 2
Which statement can be used to show that these expressions are equivalent?
A. The expressions name the same number regardless of the value
of x.
B. Both expressions involve addition,
C. Each expression includes the term 3x.
D. 3x + 4 can be rewritten as 2 + 3x + 2 using the distributive
property

Answer 1

Expressions A and B are equivalent because Expression B simplifies to 3x + 4, which is the same as Expression A. The correct statement is A: The expressions name the same number regardless of the value of x.

Step-by-step explanation:

You've asked which statement can be used to show that the expressions 3x + 4 and 2 + 3x + 2 are equivalent. To determine if the expressions are equivalent, we need to simplify Expression B and then compare it with Expression A.

Let's simplify Expression B:

1. Expression B is 2 + 3x + 2.
2. Combine the like terms (2 and 2) to get 4 + 3x.
3. Rearrange the terms to get 3x + 4, which matches Expression A.

Now, we know that the correct answer is A, as both expressions name the same number regardless of the value of x. This is supported by the commutative property which states that you can add numbers in any order and still get the same result (A+B=B+A).