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Nilai undefined yang memenuhi persamaan begin mathsize 14px style open vertical bar 3 italic x plus 1 close vertical bar plus 5 equals open vertical bar italic x minus sign 5 close vertical bar plus 9 end style adalah ....

  1. undefined atau begin mathsize 14px style italic x equals 2 end style 

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

  3. undefined atau begin mathsize 14px style italic x equals 5 end style 

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

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 3 italic x plus 1 close vertical bar plus 5 end cell equals cell open vertical bar italic x minus sign 5 close vertical bar plus 9 end cell row cell open vertical bar 3 italic x plus 1 close vertical bar minus sign open vertical bar italic x minus sign 5 close vertical bar end cell equals 4 end table end style

Ingat bahwa

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

Oleh karena itu,

begin mathsize 14px style open vertical bar 3 italic x plus 1 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell 3 italic x plus 1 comma end cell cell text untuk  end text 3 italic x plus 1 greater or equal than 0 end cell row cell negative sign open parentheses 3 italic x plus 1 close parentheses comma end cell cell text untuk  end text 3 italic x plus 1 less than 0 end cell end table close end style 

dan

begin mathsize 14px style open vertical bar italic x minus sign 5 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell italic x minus sign 5 comma end cell cell text untuk  end text italic x minus sign 5 greater or equal than 0 end cell row cell negative sign open parentheses italic x minus sign 5 close parentheses comma end cell cell text untuk  end text italic x minus sign 5 less than 0 end cell end table close end style 

atau

begin mathsize 14px style open vertical bar 3 italic x plus 1 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell 3 italic x plus 1 comma end cell cell text untuk  end text italic x greater or equal than minus sign 1 third end cell row cell negative sign open parentheses 3 italic x plus 1 close parentheses comma end cell cell text untuk  end text italic x less than minus sign 1 third end cell end table close end style                                       

dan

begin mathsize 14px style open vertical bar italic x minus sign 5 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell italic x minus sign 5 comma end cell cell text untuk  end text italic x greater or equal than 5 end cell row cell negative sign open parentheses italic x minus sign 5 close parentheses comma end cell cell text untuk  end text italic x less than 5 end cell end table close end style 

Perhatikan garis bilangan berikut.

 

Untuk begin mathsize 14px style italic x less than minus sign 1 third end style, maka begin mathsize 14px style open vertical bar 3 italic x plus 1 close vertical bar equals minus sign open parentheses 3 italic x plus 1 close parentheses end style dan begin mathsize 14px style open vertical bar italic x minus sign 5 close vertical bar equals minus sign open parentheses italic x minus sign 5 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 3 italic x plus 1 close vertical bar minus sign open vertical bar italic x minus sign 5 close vertical bar end cell equals 4 row cell negative sign open parentheses 3 italic x plus 1 close parentheses minus sign open parentheses negative sign open parentheses italic x minus sign 5 close parentheses close parentheses end cell equals 4 row cell negative sign 3 italic x minus sign 1 plus italic x minus sign 5 end cell equals 4 row cell negative sign 2 italic x minus sign 6 end cell equals 4 row cell negative sign 2 italic x end cell equals 10 row italic x equals cell negative sign 5 end cell end table end style 

Karena begin mathsize 14px style negative sign 5 end style kurang dari begin mathsize 14px style negative sign 1 third end style, maka begin mathsize 14px style italic x equals minus sign 5 end style memenuhi persamaan.

Untuk begin mathsize 14px style negative sign 1 third less or equal than italic x less than 5 end style, maka begin mathsize 14px style open vertical bar 3 italic x plus 1 close vertical bar equals 3 italic x plus 1 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 3 italic x plus 1 close vertical bar minus sign open vertical bar italic x minus sign 5 close vertical bar end cell equals 4 row cell open parentheses 3 italic x plus 1 close parentheses minus sign open parentheses negative sign open parentheses italic x minus sign 5 close parentheses close parentheses end cell equals 4 row cell 3 italic x plus 1 plus italic x minus sign 5 end cell equals 4 row cell 4 italic x minus sign 4 end cell equals 4 row cell 4 italic x end cell equals 8 row italic x equals 2 end table end style 

Karena 2 berada pada rentang undefined, maka begin mathsize 14px style italic x equals 2 end style memenuhi persamaan.

Untuk begin mathsize 14px style italic x greater or equal than 5 end style, maka undefined dan begin mathsize 14px style open vertical bar italic x minus sign 5 close vertical bar equals italic x minus sign 5 end style.

Oleh karena itu,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 3 italic x plus 1 close vertical bar minus sign open vertical bar italic x minus sign 5 close vertical bar end cell equals 4 row cell open parentheses 3 italic x plus 1 close parentheses minus sign open parentheses italic x minus sign 5 close parentheses end cell equals 4 row cell 3 italic x plus 1 minus sign italic x plus 5 end cell equals 4 row cell 2 italic x plus 6 end cell equals 4 row cell 2 italic x end cell equals cell negative sign 2 end cell row italic x equals cell negative sign 1 end cell end table end style 

Karena begin mathsize 14px style negative sign 2 end style kurang dari 5, maka begin mathsize 14px style italic x equals minus sign 2 end style tidak memenuhi persamaan pada kasus ini.

Oleh karena itu, nilai begin mathsize 14px style italic x end style yang memenuhi persamaan begin mathsize 14px style open vertical bar 3 italic x plus 1 close vertical bar plus 5 equals open vertical bar italic x minus sign 5 close vertical bar plus 9 end style adalah undefined atau undefined.

Jadi, jawaban yang tepat adalah B.

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