Matematika SMA

 Matematika  

Tentukn himpunan penyelesaian pertidaksamaan berikut jika peubah pada himpunan bilangan cacah?
1. 12-6y ≥ -6

2. 3(2t-1) ≤ 2t+9

3. 2(x-30) < 4(x-2)

4. 6-2(y-3) ≤ 3(2y-4)

5. 6x-3/3 ≥ 2(x+3)/2
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 Jawaban Terbaik:  1. 12-6y ≥ -6
....-6y ≥ -6 - 12
....-6y ≥ -18
......y ≤ -18/-6
......y ≤ 3
HP = {0, 1, 2, 3}

2. 3(2t - 1) ≤ 2t + 9
.....6t - 3 ≤ 2t + 9
.....6t - 2t ≤ 9 + 3
.....4t ≤ 12
.......t ≤ 12/4
.......t ≤ 3
HP = {0, 1, 2, 3}

3. 2(x - 30) < 4(x - 2)
....2x - 60 < 4x - 8
....2x - 4x < -8 + 60
......-2x < 52
........x > 52/-2
........x > -26
HP = {...}

4. 6 - 2(y - 3) ≤ 3(2y - 4)
....6 - 2y + 6 ≤ 6y - 12
....-2y - 6y ≤ -12 + 12
.......-8y ≤ 0
..........y ≥ 0
HP = {0, 1, 2, 3, ....}

5. 6x - 3 /3 ≥ 2(x + 3)/2
....6x - 3 /3 ≥ x + 3
-----------------------------dikali 3
....6x - 3 ≥ 3x + 9
....6x - 3x ≥ 9 + 3
........3x ≥ 12
...........x ≥ 12/3
...........x ≥ 4
HP = {4, 5, 6, ......}