Question

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(x – 5) (x + 9)(x – 8) < 0 solve inequality​

Answer 1

Given:-

(x+9)(x−5)(x−8)<0

Let f(x)=(x−5)(x+9)(x−8)

Here the critical points are −9,5,8

• Plot these points on a number line. These points divide the number line into 4 intervals.

Now,

pick a point from each interval and find the sign of f(x)

• f(−10)<0

• f(0)>0

• f(6)<0

• f(9)>0

Since the inequality given in the question is ′ < ′

the solution is the interval containing

′− ′ sign

Thus, x lies in the interval

(−∞ ,−9)∪(5,8)

Answer 2

EXPLANATION.

Inequality of the equation.

⇒ (x - 5)(x + 9)(x - 8) < 0.

As we know that,

First we find the zeroes of the equation, we get.

⇒ x - 5 = 0.

⇒ x = 5. - - - - - (1).

⇒ x + 9 = 0.

⇒ x = -9. - - - - - (2).

⇒ x - 8 = 0.

⇒ x = 8. - - - - - (3).

Put the values in the wavy curve method, we get.

⇒ x ∈ (-∞,-9) ∪ (5,8).

MORE INFORMATION.

Domain = Domain of relation is collection of elements of the first set which are participating in the correspondence that is it is set of all pre-images under the relation R.

Co-Domain = All elements of set Y irrespective of whether they are related with any element of X or not constitute Co-domain.

Range = Range of relation is a set of those elements of set Y which are participating in correspondence that is set of all images.