P and q are complex numbers such that |p|=3/4x+2, |q|=2x+1, and |p+q|=2/3x-2. On what interval must x fall on?

Answer choices:

a. (-infinity, - 13/5]

b.[3, infinity)

c.[-8/3,-13/5]

d.[-8/3, - 1/2]

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)