Question

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

Answer 1

Answer = a - 7 _< 5 and a - 7 >_ - 5

3rd one is correct

or C is correct

Answer 2

Answer: Choice C

`a-7 \le 5` (a-7 is less than or equal to 5)
and

`a-7 \ge -5` (a-7 is greater than or equal to -5)

----------------------------------------------------

Step-by-step explanation:


`|a-7| \le 5` is the same as
`-5 \le a-7 \le 5`

We can use the rule that if
`|x| \le k` then
`-k \le x \le k` where k is any positive number

After we get
`-5 \le a-7 \le 5`, we break it down into two pieces. The first piece is
`-5 \le a-7` while the second piece is
`a-7 \le 5`

Flip the two sides of
`-5 \le a-7` to get
`a-7 \ge -5`

So we have
`a-7 \le 5` and
`a-7 \ge -5`

That's why the answer is choice C

Side Note: we must use the connector "and" instead of "or". Both parts of
`a-7 \le 5` and
`a-7 \ge -5` need to be true, instead of just one part only. This is why we can rule out choice B due to the "or" connector.