Question

Which equations have the same value of x as 2/3(6x+12) = -24? Select two options.A: 4x+8=-24B: 9x+18=-24C: 4x=-16D: 18x+36/2=-24E: 4X=-32

Answer 1

The equation given is:

`(2)/(3)(6x+12)=-24`

Solving for x:

`\begin{gathered} (2)/(3)(6x+12)=-24 \\ 4x+8=-24 \\ 4x=-24-8 \\ 4x=-32 \\ x=-8 \end{gathered}`

Now, let's solve all the equations and see which one(s) have a solution x = -8.

-- 4x +8 = - 24

4x = -32

x = -8

YES!

-- 9x+18 = - 24

9x = -42

x = -42/9

x = -14/3

No!

-- 4x = - 16

x = -4

No!

--

`\begin{gathered} (18x+36)/(2)=-24 \\ 9x+18=-24 \\ 9x=-42 \\ x=-(42)/(9) \\ x=-(14)/(3) \end{gathered}`

No!

-- 4x = -32

x = -32/4

x = -8

Yes!

Answer
`\begin{gathered} 4x+8=-24 \\ \text{and} \\ 4x=-32 \end{gathered}`