tell whether these pair of expressions are equivalent

Question

-4 plus the quantity x-3 divided by 2 -3 and the quantity x-3 divided by 2 + negative 7

Answer 1

Yes, these pair of expressions are equivalent.

To prove this, we can simplify both expressions:
1) -4 plus the quantity x-3 divided by 2 -3
= (-4 + x-3) / 2 - 3
= (x-7) / 2 - 3

2) The quantity x-3 divided by 2 + negative 7
= (x-3)/2 + (-7)
= (x-3)/2 - 7

As we can see, both expressions simplify to (x-7)/2 - 3 and (x-3)/2 - 7 respectively. Thus, they are equivalent.