Question

Express $a\ge -3$ and $a<3$ as a compound inequality.

• A. $-3\le a<3$
• B. $-3\le a\le 3$
• C. $-3\ge a<3$
• D. $-3\le a\ge 3$

Answer 1

The correct option is A $-3\le a<3$

Given, $a>-3$ and $a\le 3$

Compound inequality is a combination of two separate inequalities that satisfies both the condition of the two inequalities.

Step 1: $a\ge -3$ can be represented as $-3\le a$
$\to$ $a$ is greater than -3 as well as equal to -3.
Let's represent this on the number line, where closed circle will be on -3.

Step 2: $a<3$
$\to$Since in the inequality 3 is not included as $a$ is strictly less than 3.

Let's represent this on the number line, where open circle will be on 3.

Combinining both the inequalities:
$\Rightarrow -3\le a<3$

This compound inequality represents $a$ is greater than or equal to $-3$ and less than $3$ simultaneously.

$\therefore$ $a$ lies from $-3$ to $3$, including -3 and excluding $3$.