Question

Express $a\ge -2$ and $a\le 1$ as a compound inequality.

• A. $-2\le a\le 1$
• B. $-2\le a\ge 1$
• C. $-2\ge a\le 1$
• D. $-2<a\le 1$

Answer 1

The correct option is A $-2\le a\le 1$

Given, $a>-2$ and $a\le 1$

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

Step 1: $a\ge -2$ can be represented as $-2\le a$
$\to$ a is greater than -2 as well as equal to -2.
Let's represent this on the number line, where closed circle will be on -2.

Step 2: $a\le 1$
$\to$ a is less than or equal to 1.
Let's represent this on the number line, where closed circle will be on 1.

Combining both the inequalities:
$\Rightarrow -2\le a\le 1$

This compound inequality represents $a$ is greater than or equal to $-2$ and less than or equal to $1$ simultaneously.

$\therefore$ $a$ lies from $-2$ to $1$, including -2 and including $1$.