Question

solve for x : (x-2) (x-4) < 0

• A. (2, 4)
• B. (, 2] U [4,)
• C. [2, 4]
• D. [4,)

Answer 1

The correct option is A

(2, 4)

(x-2) (x-4) = 0 $\Rightarrow$ x = 2,4

Representing on the number line,

(i)When x > 4,(x- 4) > 0 and (x - 2) > 0

$\Rightarrow$ (x - 2) (x - 4) > 0 ------------(1)

(ii)When 2< x <4,(x - 4) < 0 and x - 2 > 0

$\Rightarrow$ (x - 2) (x - 4) < 0 ------------(2)

(iii)When x < 2,(x - 4) < 0 and (x - 2) < 0

$\Rightarrow$ (x - 2) (x - 4) > 0 ------------(3)

So,given expression takes positive value for x ∈ ($-\infty$,2) U (4,$\infty$) and takes negative values for x ∈ (2,4)

On a number line, this is represented as

Hence,the values of x for (x-2)(x-4) < 0 is x ∈ (2,4)