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Nilai x yang memenuhi persamaan  adalah ....

Pertanyaan

Nilai begin mathsize 14px style x end style yang memenuhi persamaan begin mathsize 14px style 2 open vertical bar x plus 7 close vertical bar minus sign 3 open vertical bar 2 x minus sign 3 close vertical bar plus 2 x equals 5 end style adalah ....

  1. begin mathsize 14px style x equals 0 end style atau Error converting from MathML to accessible text. 

  2. undefined atau begin mathsize 14px style x equals 14 over 3 end style 

  3. begin mathsize 14px style x equals minus sign 9 end style atau undefined 

  4. begin mathsize 14px style x equals minus sign 14 over 3 end style atau undefined 

  5. begin mathsize 14px style x equals 0 comma space x equals 14 over 3 end style atau begin mathsize 14px style x equals 9 end style   

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 open vertical bar x plus 7 close vertical bar minus sign 3 open vertical bar 2 x minus sign 3 close vertical bar plus 2 x end cell equals 5 row cell 2 open vertical bar x plus 7 close vertical bar minus sign 3 open vertical bar 2 x minus sign 3 close vertical bar end cell equals cell negative sign 2 x plus 5 end cell end table end style 

Ingat bahwa

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

Oleh karena itu,

begin mathsize 14px style open vertical bar x plus 7 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell x plus 7 comma end cell cell text untuk  end text x plus 7 greater or equal than 0 end cell row cell negative sign open parentheses x plus 7 close parentheses comma end cell cell text untuk  end text x plus 7 less than 0 end cell end table close end style 

dan

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

atau

begin mathsize 14px style open vertical bar x plus 7 close vertical bar equals open curly brackets table attributes columnalign right end attributes row cell x plus 7 comma end cell cell text untuk  end text x greater or equal than minus sign 7 end cell row cell negative sign open parentheses x plus 7 close parentheses comma end cell cell text untuk  end text x less than minus sign 7 end cell end table close end style 

dan

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

Perhatikan garis bilangan berikut.

 

Untuk begin mathsize 14px style x less than minus sign 7 end style, maka begin mathsize 14px style open vertical bar x plus 7 close vertical bar equals minus sign open parentheses x plus 7 close parentheses end style dan begin mathsize 14px style open vertical bar 2 x minus sign 3 close vertical bar equals minus sign open parentheses 2 x minus sign 3 close parentheses end style.

Oleh karena itu,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 open vertical bar x plus 7 close vertical bar minus sign 3 open vertical bar 2 x minus sign 3 close vertical bar end cell equals cell negative sign 2 x plus 5 end cell row cell 2 open parentheses negative sign open parentheses x plus 7 close parentheses close parentheses minus sign 3 open parentheses negative sign open parentheses 2 x minus sign 3 close parentheses close parentheses end cell equals cell negative sign 2 x plus 5 end cell row cell negative sign 2 x minus sign 14 plus 6 x minus sign 9 end cell equals cell negative sign 2 x plus 5 end cell row cell 4 x minus sign 23 end cell equals cell negative sign 2 x plus 5 end cell row cell 6 x end cell equals 28 row x equals cell 14 over 3 end cell end table end style 

Karena begin mathsize 14px style 14 over 3 end style tidak kurang dari begin mathsize 14px style negative sign 7 end style, maka undefined tidak memenuhi persamaan pada kasus ini.

Untuk begin mathsize 14px style negative sign 7 less or equal than x less than 3 over 2 end style , maka begin mathsize 14px style open vertical bar x plus 7 close vertical bar equals x plus 7 end style dan undefined.

Oleh karena itu,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 open vertical bar x plus 7 close vertical bar minus sign 3 open vertical bar 2 x minus sign 3 close vertical bar end cell equals cell negative sign 2 x plus 5 end cell row cell 2 open parentheses x plus 7 close parentheses minus sign 3 open parentheses negative sign open parentheses 2 x minus sign 3 close parentheses close parentheses end cell equals cell negative sign 2 x plus 5 end cell row cell 2 x plus 14 plus 6 x minus sign 9 end cell equals cell negative sign 2 x plus 5 end cell row cell 8 x plus 5 end cell equals cell negative sign 2 x plus 5 end cell row cell 10 x end cell equals 0 row x equals 0 end table end style 

Karena 0 berada pada rentang undefined, maka undefined memenuhi persamaan.

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

Oleh karena itu,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 open vertical bar x plus 7 close vertical bar minus sign 3 open vertical bar 2 x minus sign 3 close vertical bar end cell equals cell negative sign 2 x plus 5 end cell row cell 2 open parentheses x plus 7 close parentheses minus sign 3 open parentheses 2 x minus sign 3 close parentheses end cell equals cell negative sign 2 x plus 5 end cell row cell 2 x plus 14 minus sign 6 x plus 9 end cell equals cell negative sign 2 x plus 5 end cell row cell negative sign 4 x plus 23 end cell equals cell negative sign 2 x plus 5 end cell row cell negative sign 2 x end cell equals cell negative sign 18 end cell row x equals 9 row blank blank blank end table end style 

Karena 9 lebih dari begin mathsize 14px style 3 over 2 end style, maka undefined memenuhi persamaan.

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

Jadi, jawaban yang tepat adalah A.

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