Question

6. Gambarkan dalam garis bilangan dan notasi pertidaksamaan masing masing nilai mutlak berikut ini: a. |x| ≤ 3 c. |x – 4| 3 d. |x – 4 | ≥ 1

Answer 1

Given  : | x| ≤ 3   , |x – 4 | ≥ 1

To find :  x Values range

Solution:

|x| ≤ 3    

| x | = x    when x ≥ 0

| x | = -x  when x < 0

when x ≥ 0 then x ≤ 3  

=>   0 ≤ x  ≤ 3  

when x < 0  then - x  ≤ 3  

=> x ≥ - 3

- 3 ≤ x  < 0

- 3 ≤ x  < 0    &  0 ≤ x  ≤ 3  

=>   - 3  ≤ x   ≤ 3  

|x| ≤ 3  => - 3  ≤ x   ≤ 3  

x ∈  [ - 3 ,  3 ]

|x – 4 | ≥ 1

when x - 4  ≥ 0  =>  x   ≥ 4

then x – 4  ≥ 1   => x ≥ 5

combining both x ≥ 5

when x - 4  <  0  =>  x  < 4

-(x - 4)  ≥ 1

=> x - 4 ≤ - 1

=> x ≤  3

x ≤  3  

x ≤  3     ,  x ≥ 5  

x ∈ R - (3 , 5)   or (-∞ , 3] ∪ [ 5 , ∞)

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