Question

Sonia got greater than or equal to –8 marks but less than or equal to 19 marks, while Tony got less than or equal to 26 marks but greater than or equal to 9 marks in a tough quiz.
Determine the compound inequality in terms of $x$, which represents the marks that they obtained.

Answer 1

Given:

Sonia got marks greater than or equal to –8 but less than or equal to 19.

We can represent this as:
$-8\le x\le 19$

Tony got marks less than or equal to 26 but greater than or equal to 8.

We can represent this as:
$8\le x\le 26$

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

Step 1: $x\ge -8$ and $x\le 19$ can be represented as $x$ greater than –8 and $x$ less than or equal to 19.

This can be represented as:



Step 2: $8\le x\le 26$

$\to$ $x$ is less than or equal to 26 and greater than 8.

This can be represented as:


Step 3: Combining both the inequalities
$\Rightarrow 9\le x\le 19$


This compound inequality represents "$x$ is greater than or equal to $9$" and "less than or equal to $19$" simultaneously.

$\therefore$ $x$ lies between 9 and 19, including both 9 and 19.