Answer: B
( - 3 , infinity )
Step-by-step explanation:
Given that
|p| = 3/4x+2
|q| = 2x+1
|p+q| = 2/3x-2
|p| + |q| = |p+q|
That is
3/4x+2 + 2x+1 = 2/3x-2
(3x + 8)/4 + 2x + 1 = (2x - 6)/3
(3x + 8 + 8x + 4)/4 = (2x - 6)/3
Cross multiply
9x + 24 + 24x + 12 = 8x - 24
Collect the like terms
33x + 36 = 8x - 24
33x - 8x = - 24 - 36
25x = - 60
X = -60/25
X = - 2.4
X should fall on the interval of
( -3, infinity)
