Question

Nilai Mutlak , tolong bantu menggunakan cara . terimakasih .

Answer 1

|x-2| > 4/(|x-2|+3)
|x-2||x-2|+3 > 4
|x-2||x-2| > 1
(|x-2|)² > 1
|x²-4x+4| > 1
=> x²-4x+4 > 1
x²-4x+3 > 0
(x-1)(x-3) > 0
x = 1 atau x = 3
uji : x = 0
-1(-3) > 0
3 > 0 (memenuhi)
x = 4
(4-1)(4-3) > 0
3 > 0 (memenuhi)
x = -1
(-1-1)(-1-3) > 0
(-2)(-4) > 0
8 > 0 (memenuhi)
x < 1 atau x > 3

=> x²-4x+4 < -1
x²-4x+5 < 0
(x-5)(x+1) < 0
x = 5 atau x = -1
uji : x= 0
(-5)(1) < 0
-5 < 0 (memenuhi)
x = 1
(1-5)(1+1) < 0
(-4)(2) < 0
-8 < 0 (memenuhi)
-1 < x < 5
Cek sekali lagi:
x = -1
|-1-2| > 4/(|-1-2|+3)
|-3| > 4/(|-3|+3)
3 > 4/(3+3)
3 > 4/6 (memenuhi)
x = 0
|0-2| > 4/(|0-2|+3)
|-2| > 4/(|-2|+3)
2 > 4/(2+3)
2 > 4/5 (memenuhi)
x = 2
|2-2| > 4/(|2-2|+3)
0 > 4/(0+3)
0 > 4/3 (tidak memenuhi)
x = 4
|4-2| > 4/(|4-2|+3)
|2| > 4/(|4-2|+3)
|2| > 4/(2+3)
2 > 4/5 (memenuhi)
x = 5
|5-2| > 4/(|5-2|+3)
3 > 4/(3+3)
3 > 4/6 (memenuhi)
=> x < 1 atau x > 3