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Matematika wajib kelas 10 persamaan nilai mutlak

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Persamaan Nilai Mutlak
k
Bentuk Umum PLSV yang Memuat Nilai
Mutlak
|ax + b| = c
Nilai mutlak dari suatu bilangan x (|x|) dapat diartikan sebagai jarak
bilangan tersebut terhadap titik 0 pada garis bilangan, dengan tidak
memperhatikan arahnya.
Contoh: Tentukan penyelesaian |x| = 5.
|x| = 5 berarti 2 penyelesaian, karena terdapat 2 bilangan yang jaraknya
terhadap 0 adalah 5: x = 5, x = -5.
Definisi Persamaan Nilai Mutlak
|ax + b| = {ax + b, jika ax + b ≥ 0 → x ≥ -b/a, -(ax + b), jika ax + b < 0 → x
< -b/a}.
Sifat-Sifat Nilai Mutlak
•
|x| ≥ 0
•
|x| = |-x|
•
|x - y| = |y - x|
•
|x| = √|x
2
|
•
|x
2
| = x
2
•
Jika |x|<|y|, maka x
2
< y
2
.
•
|xy| = |x| |y|
•
|x/y| = |x|/|y|; y ≠ 0
•
|x - y| = |x|-|y|
•
|x + y| = |x|+|y|

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Contoh Soal
1.
|x + 5| = 1
|x + 5| = 1 {x + 5 = 1, x ≥ -5, -(x + 5) = 1, x < -5.
Untuk x ≥ 5, maka berlaku:
x + 5 = 1
x = -4
Untuk x < -5, maka berlaku:
-(x + 5) = 1
-x – 5 = 1
x = -6
HP = {-6, -4}
2.
|3 – 2x| = 5
(3 – 2x)
2
= 5
2
(3 – 2x)
2
- 5
2
= 0
(3 – 2x)
2
- 5
2
= 0
(3 – 2x – 5)
(3 – 2x + 5)
= 0
(-2x – 2) (-2x + 8) = 0
(x + 1) (x – 4) = 0
x
1
= -1, x
2
= 4
HP = {-1, 4}
3.
|x - 3| = -2
|x - 3| = -2 (TM), karena nilai mutlak tidak pernah menghasilkan nilai
negatif.
4.
|2x - 1| + x = 3
(2x – 1)
2
+ x
2
= 3
2
(2x – 1)
2
= (3
- x)
2
(2x – 1)
2
- (3
- x)
2
= 0
((2x – 1)+ (3
- x)) ((2x – 1)-(3
- x)) = 0
(2x – 1 +3
- x) (2x – 1 - 3
+ x) = 0
(x + 2) (3x - 4) = 0
x
1
= -2, x
2
= 4/3
HP = {-2, 4/3}
5.
|x - 3| = |3x + 1|
(x – 3)
2
= (3x + 1)
2
(x – 3)
2
= (3x + 1)
2
(x – 3)
2
- (3x + 1)
2
= 0

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aaaaa Persamaan Nilai Mutlak k Bentuk Umum PLSV yang Memuat Nilai Mutlak |ax + b| = c Nilai mutlak dari suatu bilangan x (|x|) dapat diartikan sebagai jarak bilangan tersebut terhadap titik 0 pada garis bilangan, dengan tidak memperhatikan arahnya. Contoh: Tentukan penyelesaian |x| = 5. |x| = 5 berarti 2 penyelesaian, karena terdapat 2 bilangan yang jaraknya terhadap 0 adalah 5: x = 5, x = -5. Definisi Persamaan Nilai Mutlak |ax + b| = {ax + b, jika ax + b ≥ 0 → x ≥ -b/a, -(ax + b), jika ax + b < 0 → x < -b/a}. Sifat-Sifat Nilai Mutlak • • • • • • • • • • |x| ≥ 0 |x| = |-x| |x - y| = |y - x| |x| = √|x2| |x2| = x2 Jika |x| ...
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