Himpunan penyelesaian dari pertidaksamaan 0<∣x − 3∣≤3 adalah ....

Pertanyaan

Himpunan penyelesaian dari pertidaksamaan begin mathsize 12px style 0 less than open vertical bar x space minus space 3 close vertical bar less or equal than 3 end style adalah ....undefined 

  1. begin mathsize 14px style open curly brackets x left enclose space 0 less than x less than 3 end enclose space atau space 3 less than x less or equal than 6 comma space x element of straight real numbers close curly brackets end style 

  2. open curly brackets x left enclose space 0 less or equal than x less than 3 end enclose space atau space 3 less than x less or equal than 6 comma space x element of straight real numbers close curly brackets 

  3.  open curly brackets x left enclose space 0 less or equal than x less or equal than 3 end enclose space atau space 3 less than x less or equal than 6 comma space x element of straight real numbers close curly brackets 

  4. open curly brackets x left enclose space 0 less or equal than x less or equal than 3 end enclose space atau space 3 less than x less than 6 comma space x element of straight real numbers close curly brackets 

  5. open curly brackets x left enclose space 0 less than x less than 3 end enclose space atau space 3 less than x less than 6 comma space x element of straight real numbers close curly brackets 

P. Anggrayni

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Kondisi (i) jika begin mathsize 14px style left parenthesis x minus 3 right parenthesis greater than 0 end style 

Syarat :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis x minus 3 right parenthesis end cell greater or equal than 0 row x greater or equal than 3 end table end style  

Maka :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row 0 less than cell open parentheses x minus 3 close parentheses less or equal than 3 end cell row 3 less than cell x less or equal than 6 space left parenthesis tambahkan space 3 space pada space setiap space ruas right parenthesis end cell row 3 less than cell x less or equal than 6 space left parenthesis memenuhi space syarat space kondisi space left parenthesis straight i right parenthesis end cell end table end style 

Kondisi (ii) jika begin mathsize 14px style x minus 3 less than 0 end style   

Syarat :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 3 end cell less than 0 row x less than 3 end table end style 

Maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row 0 less than cell negative open parentheses x minus 3 close parentheses less or equal than 3 end cell row 0 less than cell negative x plus 3 less or equal than 3 end cell row cell negative 3 end cell less than cell negative x less or equal than 0 end cell row 3 greater than cell x greater or equal than 0 space dikalikan space negatif space tanda space berubah end cell row 0 less or equal than cell x less than 3 space memenuhi space syarat space left parenthesis ii right parenthesis end cell end table end style  

Dengan demikian, himpunan penyelesaian dari pertidaksamaan tersebut yaitu:

open curly brackets x left enclose space 0 less or equal than x less than 3 end enclose space atau space 3 less than x less or equal than 6 comma space x element of straight real numbers close curly brackets 

Oleh karena itu, jawaban yang benar adalah B.

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