Question

Set of values of x satisfying the inequality (x-3)? (2x+5)(x-7) < 0 is : (x2+x+1)(3x+6)2​

Answer 1

Answer:

Given that,

(x−1)(x−2)<0 and (3x−7)(2x−3)>0

(3x−7)(2x−3)>0 can be written as

⇒3(x−

3

7

)2(x−

2

3

)>0

⇒(x−

3

7

)(x−

2

3

)>0

So, according to this equation we have,

⇒x<

2

3

and x>

3

7

Now consider (x−1)(x−2)<0

So, according to this equation we have,

⇒1<x<2

Considering these constraints we have

⇒x lies in (1,

2

3

)

Answer 2

Answer:

(3x−7)(2x−3)>0 can be written as

⇒3(x−37)2(x−23)>0

⇒(x−37)(x−23)>0

So, according to this equation we have,

⇒x<23  and x>37

Now consider (x−1)(x−2)<0  

So, according to this equation we have,

⇒1<x<2

Considering these constraints we have 

⇒x lies in (1,23)