Question

Express $y>-1$ and $y\le 3$ as a compound inequality.

• A. $-1<y<3$
  
• B. $-1<y\le 3$
  
• C. $-1\le y\le 3$
  
• D. $-1\le y<3$
  

Answer 1

The correct option is B $-1<y\le 3$


Given, $y>-1$ and $y\le 3$

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

Step 1: $y>-1$ can be represented as $-1<y$
$\to$ y is greater than -1 but not equal to -1.

Step 2: $y\le 3$
$\to$ y is less than or equal to 3.

Step 3: Combining both the inequalities:
$\Rightarrow -1<y\le 3$

This compound inequality represents $y$ is greater than $-1$ and less than or equal to $3$ simultaneously.

$\therefore$ $y$ lies from $-1$ to $3$, excluding -1 and including $3$.