Question

Tolong beritahu bagaimana caranya mengerjakan nomor 4

Answer 1

|3x + 1| - |2x + 4| > 10
=> |3x + 1| > |2x + 4| + 10
=> (|3x + 1|)^2 > (|2x + 4| + 10)^2
=> 9x^2 + 6x + 1 > (4x^2 + 16x + 16) + 20|2x + 4| + 100
=> 9x^2 - 4x^2 + 6x - 16x + 1 - 16 - 100 > 20|2x + 4|
=> 5x^2 - 10x - 115 > 20|2x + 4|
=> x^2 - 2x - 23 > 4|2x + 4|
=> (x^2 - 2x - 23)^2 > (4(2x + 4))^2
=> (x^2 - 2x - 23)^2 - (8x + 16)^2 > 0
=> [(x^2 - 2x - 23) + (8x + 16)] [(x^2 - 2x - 23) - (8x + 16)] > 0
=> [x^2 + 6x - 7] [x^2 - 10x - 39] > 0
=> (x + 7)(x - 1) (x - 13)(x + 3) > 0
=> x = -7 atau x = 1 atau x = 13 atau x = -3
garis bilangan
+++ (-7) --- (-3) +++ (1) --- (13) +++
karena < 0 maka ambil yg negatif
-7 < x < -3 atau 1 < x < 13