Question

(x-1)(x+2)>=(2x+4)
solve the inequality using wavy curve method (if possible)​

Answer 1

Answer:

x ∈ ( - ∞ , - 2 ] ∪ [ 3 , ∞ )

Step-by-step explanation:

Given :

( x - 1 ) ( x + 2 ) ≥ ( 2 x + 4 )

Adding ' - ( 2 x + 4 ) ' both side we get :

= > ( x - 1 ) ( x + 2 ) - ( 2 x + 4 ) ≥ 0

= > x² + 2 x - x - 2 - 2 x - 4 ≥ 0

= > x² - x - 6 ≥ 0

= > x² - 3 x + 2 x - 6 ≥ 0

= > x ( x - 3 ) + 2 ( x - 3 ) ≥ 0

= > ( x - 3 ) ( x + 2 ) ≥ 0

For critical point :

= > x - 3 = 0

= > x = 3

= > x + 2 = 0

= > x = - 2

Now plot the point on number line. We need positive portion with closed interval of critical point.

x ∈ ( - ∞ , - 2 ] ∪ [ 3 , ∞ )

Therefore , we get required answer!