Final answer:
The expression 2x + 3 is not equivalent to x/2 + 3/4 because after finding a common denominator and transforming the latter into a single fraction, the two expressions do not share the same value or format, with 2x + 3 not being a fraction.
Step-by-step explanation:
To evaluate whether 2x + 3 is an equivalent expression to x/2 + 3/4, one must compare the two expressions by making their forms comparable. The simplest way to do this is by transforming both expressions into a similar format, like a fraction, and then seeing if they share the same value.
Firstly, address the transformation of 2x + 3 into a fraction. This expression is already simplified and cannot be directly compared to a fraction. For x/2 + 3/4, you might need to find a common denominator to combine the terms into a single fraction. Here, the common denominator would be 4, as it is a multiple of both 2 and 4. Rewriting the terms with the same denominator, the expression becomes (2x· 2)/4 + 3/4, which simplifies to (4x + 3)/4.
Now, by comparing 2x + 3 and (4x + 3)/4, it is clear that they are not equivalent, as one is not a fraction and their scales differ - one is affected by a factor of 4 in the denominator. Therefore, 2x + 3 is not equivalent to x/2 + 3/4.