Question

Find the number of integers lying between $x\ge -2$ and $x\le 5$

• A. 6
• B. 7
• C. 8
• D. 9

Answer 1

The correct option is C 8

Given, $x>-2$ and $x\le 5$

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

Step 1: $x\ge -2$ can be represented as $-2\le x$
$\to$ $x$ is greater than or equal to -2. Hence there will be a closed circle on -2.

Step 2: $x\le 5$
$\to$ $x$ is less than or equal to 5. Hence there will be a closed circle on 5.

Combinining both the inequalities:
$\Rightarrow -2\le x\le 5$

This compound inequality represents $x$ is greater than or equal to $-2$ and less than or equal to $5$ simultaneously.

As $x$ is an intger:
Values of $x$: -2, -1, 0, 1, 2, 3, 4, 5 which are 8 in number.