Answer: The winning ticket is [tex]2(x-6)=-35[/tex] is equivalent to [tex]2x=-23[/tex].
Step-by-step explanation:
Let's check all the options
[tex]4(x-5)=35[/tex] is not equivalent to [tex]4x=40[/tex]
[tex]\text{since }4(x-5)=35\\\Rightarrow4x-20=35\\\Rightarrow4x=35+20\\\Rightarrow4x=55[/tex]
[tex]8(x-7)=35[/tex] is not equivalent to [tex]8x=28[/tex]
[tex]\text{since }8(x-7)=35\\\Rightarrow8x-56=35\\\Rightarrow8x=35+56\\\Rightarrow8x=91[/tex]
[tex]2(x-6)=-35[/tex] is equivalent to [tex]2x=-23[/tex]
[tex]\text{since }2(x-6)=-35\\\Rightarrow2x-12=-35\\\Rightarrow2x=-35+12\\\Rightarrow2x=-23[/tex]
[tex]9(x-6)=-35[/tex] is not equivalent to [tex]9x=-29[/tex]
[tex]\text{since }9(x-5)=-35\\\Rightarrow9x--40=-35\\\Rightarrow9x=-35+40\\\Rightarrow9x=5[/tex]
Thus, the winning ticket is [tex]2(x-6)=-35[/tex] is equivalent to [tex]2x=-23[/tex].
