Question

Eva wants to buy more than 4 pizza but less than 9 pizza. Determine the inequality in terms of $x$ which represents the number of pizza bought.

• A. $4<x<9$
  
• B. $4<x\le 9$
  
• C. $4\le x\le 9$
  
• D. $4\le x<9$
  

Answer 1

The correct option is A $4<x<9$


Given, $x$ represents the number of pizza bought.

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

Step 1: Eva wants to buy more than 4 pizza.
$\to$ $x$ is greater than 4 but not equal to 4. Hence, there is open circle on 4
$x>4$ which can also be represented as $4<x$.

Step 2: Eva wants to buy less than 9 pizza.
$\to$ $x$ is less than 9. Hence, there is closed circle on 9.
$x<9$

Step 3: Combining both the inequalities:
$\Rightarrow 4<x<9$

This compound inequality represents $x$ is less than $9$ and greater than $4$ simultaneously.

$\therefore$ $x$ lies from $4$ to $9$, excluding 4 and excluding $9$.
$\Rightarrow 4<x<9$, option (a) is correct.