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

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

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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 $a \le 3$

Answer 2

Answer:

Choice 2.  

Step-by-step explanation: