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Nilai x yang memenuhi persamaan  adalah ....

Pertanyaan

Nilai undefined yang memenuhi persamaan begin mathsize 14px style open vertical bar italic x over 3 minus sign 2 close vertical bar minus sign open vertical bar italic x over 2 plus 1 close vertical bar equals minus sign italic x over 2 minus sign 1 end style adalah ....

  1. undefined 

  2. begin mathsize 14px style italic x equals minus sign 6 end style 

  3. undefined atau begin mathsize 14px style italic x equals 6 end style 

  4. undefined atau undefined 

  5. begin mathsize 14px style italic x equals minus sign 6 comma space italic x equals minus sign 2 end style atau undefined 

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat bahwa

 

undefined 

 

Oleh karena itu,

 

begin mathsize 14px style open vertical bar italic x over 3 minus sign 2 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell italic x over 3 minus sign 2 comma end cell cell text untuk  end text italic x over 3 minus sign 2 greater or equal than 0 end cell row cell negative sign open parentheses italic x over 3 minus sign 2 close parentheses comma end cell cell text untuk  end text italic x over 3 minus sign 2 less than 0 end cell end table close end style 

 

dan

 

begin mathsize 14px style open vertical bar italic x over 2 plus 1 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell italic x over 2 plus 1 comma end cell cell text untuk  end text italic x over 2 plus 1 greater or equal than 0 end cell row cell negative sign open parentheses italic x over 2 plus 1 close parentheses comma end cell cell text untuk  end text italic x over 2 plus 1 less than 0 end cell end table close end style 

 

atau

 

begin mathsize 14px style open vertical bar italic x over 3 minus sign 2 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell italic x over 3 minus sign 2 comma end cell cell text untuk  end text italic x greater or equal than 6 end cell row cell negative sign open parentheses italic x over 3 minus sign 2 close parentheses comma end cell cell text untuk  end text italic x less than 6 end cell end table close end style 

 

dan

 

begin mathsize 14px style open vertical bar italic x over 2 plus 1 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell italic x over 2 plus 1 comma end cell cell text untuk  end text italic x greater or equal than minus sign 2 end cell row cell negative sign open parentheses italic x over 2 plus 1 close parentheses comma end cell cell text untuk  end text italic x less than minus sign 2 end cell end table close end style 

 

Perhatikan garis bilangan berikut.

 

Untuk begin mathsize 14px style italic x less than minus sign 2 end style, maka begin mathsize 14px style open vertical bar italic x over 3 minus sign 2 close vertical bar equals minus sign open parentheses italic x over 3 minus sign 2 close parentheses end style dan begin mathsize 14px style open vertical bar italic x over 2 plus 1 close vertical bar equals minus sign open parentheses italic x over 2 plus 1 close parentheses end style.

Oleh karena itu,

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar italic x over 3 minus sign 2 close vertical bar minus sign open vertical bar italic x over 2 plus 1 close vertical bar end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell negative sign open parentheses italic x over 3 minus sign 2 close parentheses minus sign open parentheses negative sign open parentheses italic x over 2 plus 1 close parentheses close parentheses end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell negative sign italic x over 3 plus 2 plus italic x over 2 plus 1 end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell negative sign italic x over 3 plus italic x over 2 plus italic x over 2 end cell equals cell negative sign 1 minus sign 2 minus sign 1 end cell row cell negative sign fraction numerator 2 italic x over denominator 6 end fraction plus fraction numerator 3 italic x over denominator 6 end fraction plus fraction numerator 3 italic x over denominator 6 end fraction end cell equals cell negative sign 4 end cell row cell fraction numerator 4 italic x over denominator 6 end fraction end cell equals cell negative sign 4 end cell row italic x equals cell negative sign 6 end cell end table end style 

 

Karena begin mathsize 14px style negative sign 6 end style kurang dari undefined, maka undefined memenuhi persamaan.

Untuk begin mathsize 14px style negative sign 2 less or equal than italic x less than 6 end style, maka undefined dan begin mathsize 14px style open vertical bar italic x over 2 plus 1 close vertical bar equals italic x over 2 plus 1 end style.

Oleh karena itu,

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar italic x over 3 minus sign 2 close vertical bar minus sign open vertical bar italic x over 2 plus 1 close vertical bar end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell negative sign open parentheses italic x over 3 minus sign 2 close parentheses minus sign open parentheses italic x over 2 plus 1 close parentheses end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell negative sign italic x over 3 plus 2 minus sign italic x over 2 minus sign 1 end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell negative sign italic x over 3 plus 2 end cell equals 0 row cell negative sign italic x over 3 end cell equals cell negative sign 2 end cell row italic x equals 6 end table end style 

 

Karena begin mathsize 14px style 6 end style tidak berada pada rentang undefined, maka undefined tidak memenuhi persamaan pada kasus ini.

Untuk begin mathsize 14px style italic x greater or equal than 6 end style, maka begin mathsize 14px style open vertical bar italic x over 3 minus sign 2 close vertical bar equals italic x over 3 minus sign 2 end style dan undefined.

Oleh karena itu,

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar italic x over 3 minus sign 2 close vertical bar minus sign open vertical bar italic x over 2 plus 1 close vertical bar end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell open parentheses italic x over 3 minus sign 2 close parentheses minus sign open parentheses italic x over 2 plus 1 close parentheses end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell italic x over 3 minus sign 2 minus sign italic x over 2 minus sign 1 end cell equals cell negative sign italic x over 2 minus sign 1 end cell row cell italic x over 3 minus sign 2 end cell equals 0 row cell italic x over 3 end cell equals 2 row italic x equals 6 row blank blank blank end table end style 

 

Karena undefined berada pada rentang undefined, maka undefined memenuhi persamaan.

Oleh karena itu, nilai undefined yang memenuhi persamaan undefined adalah undefined atau undefined.

Jadi, jawaban yang tepat adalah D.

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