Question

What is the answe to this ?

Answer 1

`\boxed{\bf B.\: 2x-31=-2x-31}`

Explanation:

`\boxed{\bf A.\: 2x-31=2x-31}`

`\tt 2x-31=2x-31`

Since both sides are equal, there're infinitely many solutions.

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`\boxed{\bf B.\: 2x-31=-2x-31}`

`\tt 2x-31=-2x-31`

`\tt 2x=-2x`

`\tt 4x=0`

`\tt \cfrac{4x}{4}=\cfrac{0}{4}`

`\tt x=0`

One solution.

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`\boxed{\bf C.\;2x+31=2x-31}`

`\tt 2x+31=2x-31`

`\tt 2x+31-2x=2x-31-2x`

`\tt 31=-31`

Sides are not equal, meaning there is no solution.

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`\boxed{\bf D.\;2x-2=2x-31}`

`\tt 2x-2=2x-31`

`\tt 2x-2-2x=2x-31-2x`

`\tt -2=-31`

The sides are not equal, there's no solution.

Therefore, the only option is B.

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Hope this helps!