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: Hence, Option (6) and (8) are correct as their value is also "-8".Step-by-step explanation:Since we have given that [tex]\frac{2}{3}(6x+12)=-24[/tex]First we need to solve to get the value of 'x' :[tex]\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[/tex]Therefore, x=-8Now, we will check all the options :1) 4x+8=24[tex]4x+8=24\\\\4x=24-8\\\\4x=16\\\\x=\frac{16}{4}=4[/tex]2) 9x+18=-24[tex]9x+18=-24\\\\9x=-24-18\\\\9x=-42\\\\x=-4.67[/tex]3) 4x+12=-24[tex]4x+12=-24\\\\4x=-24-12\\\\4x=-36\\\\x=\frac{-36}{4}=-9[/tex]4) 18x+36/2=-24[tex]18x+18=-24\\\\18x=-24-18\\\\18x=-42\\\\x=-2.34[/tex]5) 4x=-36[tex]x=\frac{-36}{4}=-9[/tex]6) 4x=-32 [tex]x=\frac{-32}{4}=-8[/tex]7) x=-98) x=-8Hence, Option (6) and (8) are correct as their value is also "-8".