Question

Find the range of values of $x$ for the following inequation:
$(x+2)(x–3)<0;x\in R.$

• A. $-2<x<3$
• B. $-2<x<-3$
• C. $2<x<-3$
• D. $2<x<3$

Answer 1

The correct option is A $-2<x<3$

Given: $(x+2)(x–3)<0$ ​

Case 1: ​

$x+2<0\text{and}x–3>0$​

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequations.

Transfer 2 and -3 to the right side.​

$x<-3\text{and}x>5$​

It is not possible.​

Case 2:​

$x+2>0\text{and}x–3<0$​

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequations.

Transfer 2 and -3 to the right side.​

$x>-2\text{and}x<3$​

So, $-2<x<3$