Answer:
(a) 1st, 2nd
(b) 4th
Step-by-step explanation:
(a) Option 1: Expanding with the distributive property, we have
[tex]8(x+5)=8x+8\cdot 5\\~~~~~~~~~~~~=8x+40,[/tex]
which is equivalent.
Option 2: Multiplying the terms gives
[tex]8\cdot x+8\cdot 5= 8x+40[/tex],
which is equivalent.
Option 3: We don't know what x is, so there is no way to write [tex]48x[/tex] as [tex]8x+40[/tex]. This is not equivalent.
Option 4: Expanding with the distributive property gives
[tex]8(5x+1) = 8\cdot 5x+8\cdot1\\~~~~~~~~~~~~~=40x+8,[/tex]
which is not equivalent.
(b) First, we combine like terms in the given expression:
[tex]12+14y-2-y=12-2+14y-y\\~~~~~~~~~~~~~~~~~~~~~~~=10+(14-1)y\\~~~~~~~~~~~~~~~~~~~~~~~=10+13y.[/tex]
Looking at the given answer choices, only the fourth option is equivalent.
