selesaikan pertidaksamaan nilai mutlak sebagai : 1. [x/2+5]>9 2. [3x+2]<5 3.2<[2-x/2]<3 4. |x+5|<|1-9x

1.
|x/2 + 5| > 9
x/2 > 9 - 5
x/2 > 4
x > 4 × 2
x > 8

x/2 + 5 < -9
x/2 < -9 - 5
x/2 < -14
x < -14 × 2
x < -28

HPnya adalah {x < -28 dan x > 8}


2.
|3x + 2| < 5
3x < 5 - 2
3x < 3
x < 3/3
x < 1

3x + 2 > -5
3x > -5 - 2
3x > -7
x > -7/3

HPnya = {-7/3 < x < 1}

3.
2 < |2 - x/2| < 3
2 × 2 < 2 - x < 3 × 2
4 < 2 - x < 6
4 -2 < - x < 6 - 2
2 < -x < 4
2/-1 > x > 4/-1
-2 > x > -4

HPnya = {-4 < x < -2}

4.
|x + 5| < |1 - 9x|
x + 9x < 1 - 5
10x < -4
x < -4/10
x < -2/5 (benar)

-(x + 5) < (1 - 9x)
-x - 5 < 1 - 9x
- x + 9x < 1 + 5
8x < 6
x < 6/8
x < 3/4 (salah)

x + 5 < -(1 - 9x)
x + 5 < -1 + 9x
x - 9x < -1 - 5
-8x < -6
x > -6/-8
x > 3/4 (benar)

HPnya = {x < -2/5 dan x > 3/4}