Question

Tentukan HP dari persamaan nilai mutlak berikut
1. |z+5|=5
2. |6x-13|>5
3. |2x-12|-3>6

Answer 1

|z + 5| = 5
z + 5 = 5
z = 5 - 5
z = 0

z + 5 = -5
z = -5 - 5
z = -10

HP = {-10, 0}

==========

|6x - 13| > 5
6x - 13 > 5
6x > 5 + 13
6x > 18
x > 18/6
x > 3

6x - 13 < -5
6x < -5 + 13
6x < 8
x < 8/6
x < 4/3

HP = {x | x < 4/3 atau x > 3, x ∈ R}

==========

|2x - 12| - 3 > 6
|2x - 12| > 6 + 3
|2x - 12| > 9
2x - 12 > 9
2x > 9 + 12
2x > 21
x > 21/2

2x - 12 < -9
2x < -9 + 12
2x < 3
x < 3/2

HP = {x | x < 3/2 atau x > 21/2, x ∈ R}