Which conjunction or disjunction is equivalent to the open sentence |a – 7| ≤ 5? a – 7 ≥ 5 or a – 7 ≤ – 5 a – 7 ≤ 5 or a – 7 ≥ – 5 a – 7 ≤ 5 and a – 7 ≥ – 5 a – 7 ≥ 5 and a – 7 ≤ – 5

Choice C
(a-7 is less than or equal to 5)
and
(a-7 is greater than or equal to -5)

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Explanation:

is the same as

We can use the rule that if then where k is any positive number

After we get , we break it down into two pieces. The first piece is while the second piece is

Flip the two sides of to get

So we have and

That's why the answer is choice C

Side Note: we must use the connector "and" instead of "or". Both parts of and need to be true, instead of just one part only. This is why we can rule out choice B due to the "or" connector.