Which expressions are equivalent to 2 (three-fourths x + 7) minus 3 (one-half x minus 5)? Check all that apply.
-1
29
2 (three-fourths x + 7) + (negative 3) left-bracket one-half x + (negative 5) right-bracket
2 (three-fourths x) + 2 (7) + 3 (one-half x) + 3 (negative 5)
2 (three-fourths x) + 2 (7) + (negative 3) (one-half x) + (negative 3) (negative 5)

Step-by-step explanation:

The original expression given in the text is

 (1)

And we want to check to what other expressions is equivalent. First of all, we solve it by writing explicitely each term:

(2)

Let's verify each of the other expressions separately. For the first one:

We see that this is equivalent to expression (1), since the first half is identical, while in the second one, the combination "+-" can be simply written as "-", so we get

Which is equivalent to (1).

For the 2nd one:

This is not equivalent. In fact, here we have applied the distributive property to each term: however, the 3rd and 4th term are not correct, because the (3) must be negative (-3), as in the original expression.

If we write it explicitely in fact, we get

Which is different from (2).

For the 3rd one:

This one is equivalent. In fact, here we have applied the distributive property correctly. By solvign each term we get:

step-by-step explanation: