nilai pertidaksamaan mutlak no 27 Sm 28

27) |x - 2|^2 < 4|x - 2| + 12
Misal a = |x - 2|
a^2 < 4a + 12
a^2 - 4a - 12 < 0
(a - 6)(a + 2) < 0
a = 6 atau a = -2
Garis bilangan
+++ (-2) --- (6) +++
-2 < a < 6 karena a = |x - 2| selalu positif maka a < 6
|x - 2| < 6
(x - 2)^2 < 6^2
(x - 2)^2 - 6^2 < 0
(x - 2 + 6)(x - 2 - 6) < 0
(x + 4)(x - 8) < 0
x = -4 atau x = 8
Garis bilangan
+++ (-4) --- (8) +++
-4 < x < 8

28) |x - 1| + |2x - 5| < 3
|x - 1| + |2x - 2 - 3| < 3
|x - 1| + |2(x - 1) - 3| < 3
Misal a = x - 1
|a| + |2a - 3| < 3
|2a - 3| < 3 - |a|
(2a - 3)^2 < (3 - |a|)^2
4a^2 - 12a + 9 < 9 - 6|a| + a^2
6|a| < 12a - 3a^2
(6a)^2 < (12a - 3a^2)^2
(6a)^2 - (12a - 3a^2)^2 < 0
(6a + 12a - 3a^2)(6a - (12a - 3a^2)) < 0
(18a - 3a^2)(3a^2 - 6a) < 0
3a(6 - a) . 3a(a - 2) < 0
a = 0 atau a = 6 atau a = 0 atau a = 2
Garis bilangan
--- (0) --- (2) +++ (6) ---
a < 0 atau 0 < a < 2 atau a > 6
x - 1 < 0 atau 0 < x - 1 < 2 atau x - 1 > 6
x < 1 atau 1 < x < 3 atau x > 7
Jadi 1 < x < 3