Question

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

Answer 1

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)

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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.

Answer 2

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

3rd one is correct

or C is correct