Question

7. Select ALL the equations that are equivalent to the equation below:(4y +9)= 1-(5y + 8)3

Answer 1

The correct options are A, D and E

To solve this, we have the initial equation:

$\frac{4y+9}{3}=1-(5y+8)$

Now the option A is:

$\frac{4y+9}{3}=-5y-7$

The only differecnce with the first equation is on the right side. If we apply distributive propierty to the parentheses, we can see that the both equations are the same:

$1-(5y+8)\Rightarrow-5y-1-8\Rightarrow-5y-7$

Then the option A is equivalent.

In option B, the difference is that in the left side the three is there dividing anymore. But since this is an euation if we apply an operation on one side, we need to apply it on the other side. In this case, the right side is the same, so there's no way B is equaivalent.

In option C, we already apply the distributibe propierty to solve item A, and we can see that 1 - (5y + 8) = -5y - 7

Then we can rule out option C.

In option D the differecnce is in the left side of the equation. In there we can distribute the 3 that is dividing (4y + 9)

:

$\frac{4y+9}{3}\Rightarrow\frac{4}{3}y+\frac{9}{3}=\frac{4}{3}y+3$

Then option D is equivalent.

For option E, we can use the equation in option A, that w3 already know that is equivalent, and multiply by 3 on both sides, so we can get rid of the 3 dividing in the left side:

$\begin{gathered} \frac{4y+9}{3}=-5y-7 \\ 4y+9=3(-5y-7) \\ 4y+9=-15-21 \end{gathered}$

Option E is also correct.

Thus, A , D and E are the correct options.