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Bilangan real  yang memenuhi  adalah ...

Pertanyaan

Bilangan real begin mathsize 14px style x end style yang memenuhi begin mathsize 14px style fraction numerator negative 2 x plus 7 over denominator x plus 3 end fraction less or equal than 0 end style adalah ...

  1. begin mathsize 14px style x less than negative 7 over 2 end style atau begin mathsize 14px style x greater or equal than 3 end style 

  2. begin mathsize 14px style x less than negative 3 end style atau begin mathsize 14px style x greater or equal than 7 over 2 end style 

  3. begin mathsize 14px style x less or equal than negative 3 end style atau begin mathsize 14px style x greater or equal than 7 over 2 end style 

  4. begin mathsize 14px style negative 3 less than x less or equal than 7 over 2 end style 

  5. begin mathsize 14px style negative 7 over 2 less or equal than x less or equal than 3 end style 

Pembahasan Soal:

Pertidaksamaan bentuk rasional begin mathsize 14px style fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction end style, dengan begin mathsize 14px style g open parentheses x close parentheses not equal to 0 end style.

Diketahui:

Fungsi pertidaksamaan rasional begin mathsize 14px style fraction numerator negative 2 x plus 7 over denominator x plus 3 end fraction less or equal than 0 end style.

Sehingga diperoleh:

begin mathsize 14px style fraction numerator negative 2 x plus 7 over denominator x plus 3 end fraction less or equal than 0 end style

begin mathsize 14px style right enclose table row cell negative 2 x plus 7 equals 0 end cell row cell negative 2 x equals negative 7 end cell row cell x equals 7 over 2 end cell end table end enclose space table row cell x plus 3 equals 0 end cell row cell x equals negative 3 end cell row space row space end table end style

Karena begin mathsize 14px style g open parentheses x close parentheses not equal to 0 end style, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell not equal to 0 row cell x plus 3 end cell not equal to 0 row x not equal to cell negative 3 end cell end table end style 

Maka begin mathsize 14px style negative 3 end style merupakan bulatan kosong pada garis bilangan.

Uji titik di antara titik penyelesaian.

Untuk begin mathsize 14px style x equals negative 4 rightwards arrow fraction numerator negative 2 open parentheses negative 4 close parentheses plus 7 over denominator negative 4 plus 3 end fraction equals fraction numerator 8 plus 7 over denominator negative 1 end fraction equals negative 15 end style 

Untuk begin mathsize 14px style x equals 1 rightwards arrow fraction numerator negative 2 left parenthesis 1 right parenthesis plus 7 over denominator 1 plus 3 end fraction equals fraction numerator negative 2 plus 7 over denominator 4 end fraction equals 5 over 4 end style  

Untuk begin mathsize 14px style x equals 4 rightwards arrow fraction numerator negative 2 open parentheses 4 close parentheses plus 7 over denominator 4 plus 3 end fraction equals fraction numerator negative 8 plus 7 over denominator 7 end fraction equals negative 1 over 7 end style 

Karena pertidaksamaan begin mathsize 14px style less or equal than 0 end style, maka penyelesainnya yang memiliki daerah negatif.

Maka, bilangan real begin mathsize 14px style x end style yang memenuhi begin mathsize 14px style fraction numerator negative 2 x plus 7 over denominator x plus 3 end fraction less or equal than 0 end style adalah undefined atau undefined.

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 2021

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