Question

Express $x>3$ and $x\le 7$ as a compound inequality.

• A. $3<x<7$
  
• B. $3<x\le 7$
  
• C. $3\le x\le 7$
  
• D. $3\le x<7$
  

Answer 1

The correct option is B $3<x\le 7$


Given, $x>3$ and $x\le 7$

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

Step 1: $x>3$ can be represented as $3<x$
$\to$ $x$ is greater than 3 but not equal to 3. Hence, there is open circle on 3.

Step 2: $x\le 7$
$\to$ x is less than or equal to 7. Hence, there is closed circle on 7.

Step 3: Combining both the inequalities:
$\Rightarrow 3<x\le 7$

This compound inequality represents $x$ is greater than $3$ and less than or equal to $7$ simultaneously.

$\therefore$ $x$ lies between 3 and 7, excluding 3 and including 7.

Hence, option (b.) is the correct choice.