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Himpunan penyelesaian dari persamaan ∣x+2∣+4=∣2x+1∣ adalah ...

Pertanyaan

Himpunan penyelesaian dari persamaan begin mathsize 14px style open vertical bar x plus 2 close vertical bar plus 4 equals open vertical bar 2 x plus 1 close vertical bar end style adalah ...

  1. begin mathsize 14px style open curly brackets negative 3 comma space minus 5 comma space 1 third comma space 1 close curly brackets end style 

  2. undefined  

  3. begin mathsize 14px style open curly brackets negative 3 comma space 7 over 3 comma space 1 third comma space 5 close curly brackets end style 

  4. begin mathsize 14px style open curly brackets negative 3 comma space 1 third comma space 1 comma space 5 close curly brackets end style 

  5. begin mathsize 14px style open curly brackets negative 7 over 3 comma space 1 third comma space minus 3 comma space 5 close curly brackets end style 

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

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Pembahasan

Himpunan penyelesaian dari persamaan begin mathsize 14px style open vertical bar x plus 2 close vertical bar plus 4 equals open vertical bar 2 x plus 1 close vertical bar end style adalah

Sebelum menjawab pertanyaan tersebut, kita harus mengetahui konsep persamaan nilai mutlak yaitu:

begin mathsize 14px style open vertical bar x plus 2 close vertical bar equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell x plus 2 comma end cell cell x greater or equal than negative 2 end cell row cell negative x minus 2 end cell cell x less than negative 2 end cell end table close end style 

begin mathsize 14px style open vertical bar 2 x plus 1 close vertical bar equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell 2 x plus 1 comma end cell cell x greater or equal than negative 1 half end cell row cell negative 2 x minus 1 end cell cell x less than negative 1 half end cell end table close end style 

Berarti akan ada 3 kondisi:

 begin mathsize 14px style 1. space untuk space x less than negative 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative x minus 2 close parentheses plus 4 end cell equals cell open parentheses negative 2 x minus 1 close parentheses end cell row cell negative x plus 2 x end cell equals cell negative 1 plus 2 minus 4 end cell row x equals cell negative 3 end cell end table end style

begin mathsize 14px style 2. space untuk space minus 2 less or equal than x less than negative 1 half end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x plus 2 close parentheses plus 4 end cell equals cell open parentheses negative 2 x minus 1 close parentheses end cell row cell x plus 2 x end cell equals cell negative 1 minus 2 minus 4 end cell row cell 3 x end cell equals cell negative 7 end cell row x equals cell negative 7 over 3 end cell end table end style 

Tidak terpenuhi untuk begin mathsize 14px style x equals negative 7 over 3 end style karena tidak terletak begin mathsize 14px style negative 2 less or equal than x less than negative 1 half end style  

begin mathsize 14px style 3. space untuk space straight x greater or equal than negative 1 half end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x plus 2 close parentheses plus 4 end cell equals cell open parentheses 2 x plus 1 close parentheses end cell row cell x minus 2 x end cell equals cell 1 minus 2 minus 4 end cell row cell negative x end cell equals cell negative 5 end cell row x equals 5 end table end style 

 

Dengan demikian, himpunan penyelesaian dari persamaan begin mathsize 14px style open vertical bar x plus 2 close vertical bar plus 4 equals open vertical bar 2 x plus 1 close vertical bar end style adalah begin mathsize 14px style open curly brackets negative 3 comma 5 close curly brackets end style 

Jadi, tidak ada jawaban yang tepat.

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