"..the following" + plural or singular? [duplicate]

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I'm not sure of the word following should be followed by a plural or singular noun.

Which among these two sentences is grammatically correct?

"Determine the values of q, r, and s so that each of the following equations will be algebraic identities in x."

"Determine the values of q, r, and s so that each of the following equation will be algebraic identity in x."

asked Jun 9, 2020 at 11:27

AYA

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Each of implies that you are referring to several equations, so why would it not be plural?
– Kate Bunting
Commented Jun 9, 2020 at 11:35
3

Does this answer your question? "Each of them is" or "each of them are"? Also Each and every one of XYZ + singular / plural Verb and Using plural and singular with “each” before or after and We each has/have?, among others.
– FumbleFingers
Commented Jun 9, 2020 at 11:51
@KateBunting I disagree. The object complement should be in the singular exactly because we are talking about a single element in a set implied by each of.
– Eddie Kal
Commented Jun 10, 2020 at 18:08

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