Question

x(x-2)(x-5)/(x+3)(15-2x)<0​

Answer 1

EXPLANATION.

⇒ x(x - 2)(x - 5)/(x + 3)(15 - 2x) < 0.

As we know that,

We can write equation as,

⇒ x(x - 2)(x - 5)/(x + 3)(2x - 15) > 0.

Find zeroes of the equation, we get.

⇒ x = 0. - - - - - (1).

⇒ x - 2 = 0.

⇒ x = 2. - - - - - (2).

⇒ x - 5 = 0.

⇒ x = 5. - - - - - (3).

⇒ x + 3 = 0.

⇒ x = -3. - - - - - (4).

⇒ 2x - 15 = 0.

⇒ 2x = 15.

⇒ x = 7.5. - - - - - (5).

Put this points on the wavy curve method, we get.

⇒ x ∈ (-3,0) ∪ (2,5) ∪ (7.5,∞).

                                                                                                                       

MORE INFORMATION.

Power sets.

The collection of all subsets of set A is called the power set of A and is denoted by p(A).

That is,

p(A) = {x : x is a subset of A}. If x = {x₁, x₂, x₃,,,,,xₙ} then,

n(p(x)) = 2ⁿ ; n(p(p(x))) = 2²ⁿ