Question

Which equations have the same value of x as 2/3(6x+12)=-24? Check all that apply.1. 4x+8=24 2. 9x+18=-24 3. 4x+12=-24 4. 18x+36/2=-24 5. 4x=-36 6. 4x=-32 7. x=-9 8. x=-8

Answer 1

Answer: Hence, Option (6) and (8) are correct as their value is also "-8".

Step-by-step explanation:

Since we have given that

$\frac{2}{3}(6x+12)=-24$

First we need to solve to get the value of 'x' :

$\frac{2}{3}(6x+12)=-24\\\\6x+12=\frac{3}{2}\times (-24)\\\\6x+12=3\times (-12)\\\\6x+12=-36\\\\6x=-36-12\\\\6x=-48\\\\x=\frac{-48}{6}\\\\x=-8$

Therefore, x=-8

Now, we will check all the options :

1) 4x+8=24

$4x+8=24\\\\4x=24-8\\\\4x=16\\\\x=\frac{16}{4}=4$

2) 9x+18=-24

$9x+18=-24\\\\9x=-24-18\\\\9x=-42\\\\x=-4.67$

3) 4x+12=-24

$4x+12=-24\\\\4x=-24-12\\\\4x=-36\\\\x=\frac{-36}{4}=-9$

4) 18x+36/2=-24

$18x+18=-24\\\\18x=-24-18\\\\18x=-42\\\\x=-2.34$

5) 4x=-36

$x=\frac{-36}{4}=-9$

6) 4x=-32

$x=\frac{-32}{4}=-8$

7) x=-9

8) x=-8

Hence, Option (6) and (8) are correct as their value is also "-8".

Answer 2

A) 4x + 8 = -24
F) 4x = -32
H) x = -8