Question

(x-1)(x-6) is greater than 0
what are the values of x?

I will mark the best answer as Brainliest​

Answer 1

Answer:

x ∈ (-∞ , 1) U (6 , ∞).

Step-by-step explanation:

(x-1)(x-6) > 0

Consider x<1 ⇒ x-1<0

If x < 1 it is definitely less than 6( 1 < 6),

i.e x < 6 ⇒ x - 6 <0.

Hence both terms are negative.

Multiplying two negative terms gives always positive result i.e greater than zero.

Now consider 1 < x < 6,

x-1 > 0 and x-6 < 0.

One term is positive and one term is negative. So multiplying them gives us a value less than zero(negative).

Consider x >6

If x >6 it is definitely greater than 1, i.e x >1

Hence, x-1 >0 and x-6 >0.

Multiplying two positive numbers gives always a positive value i.e greater than zero.

From above discussion it is clear that x must be either less than 1 or greater than 6 for (x-1)(x-6)<0,

i.e x ∈ (-∞ , 1) U (6 , ∞).