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Himpunan penyelesaian pertidaksamaan  adalah ....

Pertanyaan

Himpunan penyelesaian pertidaksamaan fraction numerator straight x squared minus 5 straight x minus 36 over denominator 2 straight x plus 3 end fraction less or equal than 0 adalah ....

  1. open curly brackets right enclose straight x straight x less or equal than negative 4 space atau space minus 3 over 2 less or equal than straight x less or equal than 9 close curly brackets 

  2. open curly brackets right enclose straight x straight x less or equal than negative 4 space atau space minus 3 over 2 less than straight x less or equal than 9 close curly brackets 

  3. open curly brackets right enclose straight x space end enclose space minus 4 less than straight x less or equal than negative 3 over 2 space atau space straight x greater or equal than 9 close curly brackets 

  4. open curly brackets right enclose straight x space end enclose space minus 4 less or equal than straight x less or equal than negative 3 over 2 space atau space straight x greater or equal than 9 close curly brackets 

  5. open curly brackets right enclose straight x space end enclose space straight x less or equal than negative 4 space atau space straight x greater or equal than 9 close curly brackets 

Pembahasan Soal:

Pertidaksamaan bentuk rasional.

fraction numerator straight x squared minus 5 straight x minus 36 over denominator 2 straight x plus 3 end fraction less or equal than 0 left parenthesis straight x minus 9 right parenthesis left parenthesis straight x plus 4 right parenthesis left parenthesis 2 straight x plus 3 right parenthesis less or equal than 0 straight x equals 9 comma space straight x equals negative 4 comma space straight x equals negative 3 over 2 

Kita uji coba pada garis bilangan sebagai berikut :

table row cell negative negative negative end cell blank cell plus plus plus end cell blank cell negative negative negative end cell cell plus plus plus end cell row blank cell negative 4 end cell blank cell negative 3 over 2 end cell blank cell 9 space space space space space space space end cell end table 

Karena fraction numerator straight x squared minus 5 straight x minus 36 over denominator 2 straight x plus 3 end fraction less or equal than 0 maka himpunan penyelesainya adalah straight x less or equal than negative 4 space atau space minus 3 over 2 less or equal than straight x less or equal than 9. 

Syarat penyebut : 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight x plus 3 end cell not equal to 0 row straight x not equal to cell 3 over 2 end cell end table 

Dari hasil di atas maka Himpunan penyelesaian pertidaksamaan fraction numerator straight x squared minus 5 straight x minus 36 over denominator 2 straight x plus 3 end fraction less or equal than 0 adalah straight x less or equal than negative 4 space atau space minus 3 over 2 less than straight x less or equal than 9. 

Oleh karena itu, Jawaban yang benar adalah B

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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