Question

Which expression is equivalent to |a|≤3 ?

1. a ≤ –3 or a ≥ 3
2. a ≥ –3 and a ≤ 3
3. a ≥ –3 or a ≤ 3
4. a ≤ –3 and a ≥ 3

Answer 1

Choice 2.

Step-by-step explanation:

Answer 2

Answer: Choice 2.
`a \ge -3 \ \text{ and } \ a \le 3`

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Step-by-step explanation:

The rule is that if
`|a| \le k` for some positive number k, then it can be written as the compound inequality
`-k \le a \le k`. This is a shorthand way of writing the two inequalities
`a \ge -k \ \text{ and } \ a \le k` combined together.

note:
`-k \le a` is the same as
`a \ge -k`

From here, we replace k with 3

Therefore,
`|a| \le 3` turns into
`-3 \le a \le 3` which breaks down further to
`a \ge -3 \ \text{ and } \ a \le 3`

The keyword "and" is important as we can't pick one or the other. We must pick both
`a \ge -3` and also
`a \le 3`