Subject-verb agreement is the single largest rule family in the book's Writing chapter, with twelve named rules. Most sentence-correction items you'll see rest on one of them. They're worth holding in one table rather than as scattered facts.

Rule	What it says
1-2	Singular subjects take singular verbs; plural subjects take plural verbs
3	With 'or' or 'nor,' the verb agrees with the subject closer to it
4	Collective nouns (team, committee) usually take a singular verb, unless members are acting individually
5	'Each,' 'every,' 'neither,' 'either' take a singular verb
6	Some nouns look plural but are singular (mathematics, news, measles)
7	Some nouns look singular but are plural (scissors, pants, glasses)
8	Inverted sentences still agree with the true subject, even when it follows the verb
9	'Who,' 'which,' 'that' take the verb of their antecedent
10	Titles of single works or entities are singular
11	A phrase between subject and verb does not change agreement
12	Two singular subjects joined by 'and' usually take a plural verb

Rule 3 is the one to slow down on: the verb agrees with whichever subject sits closer to it, not with the first subject you read or the one that feels more important. Apply it by reading the sentence backward from the verb to the nearest noun, not forward from the start.

CORRECTED

The book's own Checkpoint 8 asks you to choose the correct version of "Neither the teacher nor the students ___ aware of the schedule change," and keys "was" as correct. Apply the book's own rule 3: the subject closer to the verb is "students," which is plural, so the verb should be "were," not "was." Checked against that rule, none of that item's four listed options is actually correct. The rule is right. The item that's supposed to demonstrate it gets it backward. Read rule 3 by finding the nearer subject first, then picking the verb that matches it, and you'll get sentences like this one right even when a worked example doesn't.