Answer:
There are no real values of x for point P to belong to the 4 quadrant
Step-by-step explanation:
The question in English is
To what real values of x does the point P (3x -6, 2x +4) belong to the 4th quadrant?
we know that
A point in the fourth Quadrant has the x-coordinate positive and the y-coordinate negative
we have the point
P (3x-6, 2x+4)
[tex]3x-6 > 0[/tex] ----> inequality A ( x-coordinate must be positive)
[tex]2x+4 < 0[/tex] ---> inequality B ( y-coordinate must be negative)
Solve Inequality A
[tex]3x-6 > 0[/tex]
[tex]3x > 6[/tex]
[tex]x > 2[/tex] -----> (2,∞)
Solve Inequality B
[tex]2x+4 < 0[/tex]
[tex]2x < -4[/tex]
[tex]x < -2[/tex] ----> (-∞,-2)
The solution of the system is
(-∞,-2) ∩ (2,∞)
therefore
The system has no solution
There are no real values of x for point P to belong to the 4 quadrant
