Tolong dibantu ya 1 . Penyelasaian dari | 5 - x | = 7 adalah 2. Nilai x yang memenuhi persamaan | x - 2 | = 5 adalah 3. Himpunan penyelesaian | x - 1 | + | 2x -

No.1
| 5 - x | = 7
(i)
5 - x = 7
x = -2
(ii)
5 - x = -7
x = 12
HP = {-2,12}

No.2
|x - 2| = 5
(i)
x - 2 = 5
x = 7
(ii)
x - 2 = -5
x = -3
HP = {-3,7}

No.3
| x - 1 | + | 2x - 4 | = 9
(i)
x - 1 + 2x - 4 = 9
3x - 5 = 9
3x = 14
x = 14/3
(ii)
x - 1 + 2x - 4 = -9
3x - 5 = -9
3x = -4
x = -4/3
HP = {-4/3 , 14/3}

No.4
|4 x - 7 | ≥ 1
(i)
4x - 7 ≥ 1
4x ≥ 1 + 7
4x ≥ 8
x ≥ 8/4
x ≥ 2
(ii)
4x - 7 ≤ -1
4x ≤ 6
x ≤ 6/4
x ≤ 3/2
HP = {x| x ≤ 3/2  atau  x ≥ 2}

No.5
|2x + 1 | ≤ 5 
-5 ≤ 2x + 1 ≤ 5
-5 - 1 ≤ 2x ≤ 5 - 1
-6 ≤ 2x ≤ 4
-3 ≤ x ≤ 2
HP = {x| -3 ≤ x ≤ 2}

No.6
| 3x + 7 | ≤ | 2x - 5 | 
(3x + 7)² ≤ (2x - 5 )²
9x² + 42x + 49 ≤ 4x² - 20x + 25
5x² + 62x + 24 ≤ 0
(5x + 2)(x + 12) ≤ 0
x ≤ -12   atau   x ≥ -2/5
HP = {x| x ≤ -12   atau   x ≥ -2/5}

No.7
| 8 - 5x | = 3
(i)
8 - 5x = 3
5x = 8 - 3
5x = 5
x = 1
(ii)
8 - 5x = -3
5x = 8 + 3
5x = 11
x = 11/5
HP = {1 , 11/5}

No.8
| 3x + 2 | = 5 
(i)
3x + 2 = 5
3x = 3
x = 1
(ii)
3x + 2 = -5
3x = -5 - 2
3x = -7
x = -7/3
HP = {-7/3 , 1}

No.9
| 2x - 5 | = | x + 3 |
4x² - 20x + 25 = x² + 6x + 9
3x² - 26x + 16 = 0
(3x - 2) (x - 8) = 0
x = 2/3  atau  x = 8
HP = {2/3 , 8}

No.10
| 4x + 1 | ≤ 9
-9 ≤ 4x + 1 ≤ 9
-10 ≤ 4x ≤ 8
-10/4 ≤ x ≤ 8/4
-5/2 ≤ x ≤ 2
HP = {x| -5/2 ≤ x ≤ 2}