Question

Which equation has no solution? A 2(x+1)=1 B 2(x+1)=2x+2 C 2(x+1)=2x+1 D 2(x+1)=2

Answer 1

C) 2(x+1)=2x+1 ( No Solution )

Explanation:

1)

`2(x+1)=1\\\cfrac{2\left(x+1\right)}{2}=(1)/(2)\\x+1=\cfrac{1}{2}\\ x+1-1=(1)/(2)-1\\\boxed{x=-(1)/(2)}`

2)

`2(x+1)=2x+2\\2x+2=2x+2\\2x+2-2=2x+2-2\\2x=2x\\2x-2x=2x-2x\\0=0`

3)

`2(x+1)=2x+1 \\2x+2=2x+1\\2x+2-2=2x+1-2\\2x=2x-1\\2x-2x=2x-1-2x\\0=-1\\\boxed{No\:Solution}`

4)

`2(x+1)=2\\\cfrac{2\left(x+1\right)}{2}=\cfrac{2}{2}\\x+1=1\\x+1-1=1-1\\x=0`

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