tentukan himpunan penyelesaian dari pertidaksamaan berikut: a) 1+x<3x+2<2+x b) 2x-1<4x<2x+1 c) 1-4x<1+3x<3+5x

a.
1 + x < 3x + 2 < 2 + x
1 + x - 2 < 3x + 2 - 2 < 2 + x - 2
-1 + x < 3x < x
-1 + x - x < 3x - x < x - x
-1 < 2x < 0
-½ < x < 0

HP. = {x | -½ < x < 0}

2.
2x - 1 < 4x < 2x + 1
2x - 1 - 2x < 4x - 2x < 2x + 1 - 2x
-1 < 2x < 1
- ½ < x < ½

HP = { x | - ½ < x < ½ }

c.
1 - 4x < 1 + 3x < 3 + 5x
1 - 1 - 4x < 1 - 1 + 3x < 3 - 1 + 5x
-4x < 3x < 2 + 5x
-4x < 3x
0 < 3x + 4x
x > 0

3x < 2 + 5x
-2 < 5x - 3x
-2 < 2x
-1 < x

HP { x | x > 0 }