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Tentukan himpunan pertidakamaan dari −6<x(x−7)≤8

Pertanyaan

Tentukan himpunan pertidakamaan dari negative 6 less than x open parentheses x minus 7 close parentheses less or equal than 8

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

 himpunan pertidakamaan dari negative 6 less than x open parentheses x minus 7 close parentheses less or equal than 8 adalah open curly brackets right enclose x space minus 1 less or equal than x less than 1 space atau space 6 less than x less or equal than 8 close curly brackets atau open square brackets negative 1 comma space 1 close parentheses union open parentheses 6 comma space 8 close square brackets.

Pembahasan

Penyelesaian pertidaksamaan fungsi negative 6 less than x open parentheses x minus 7 close parentheses less or equal than 8 dapat dipecah menjadi sebagai berikut:

  • x open parentheses x minus 7 close parentheses greater than negative 6

table attributes columnalign right center left columnspacing 0px end attributes row cell x open parentheses x minus 7 close parentheses end cell greater than cell negative 6 end cell row cell x squared minus 7 x end cell greater than cell negative 6 end cell row cell x squared minus 7 x plus 6 end cell greater than 0 row cell x squared minus x minus 6 x plus 6 end cell greater than 0 row cell x open parentheses x minus 1 close parentheses minus 6 open parentheses x minus 1 close parentheses end cell greater than 0 row cell open parentheses x minus 6 close parentheses open parentheses x minus 1 close parentheses end cell greater than 0 end table

Pembuat nol:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x minus 6 close parentheses open parentheses x minus 1 close parentheses end cell greater than 0 row cell open parentheses x minus 6 close parentheses open parentheses x minus 1 close parentheses end cell equals 0 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 6 end cell equals 0 row x equals 6 end table atau table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 1 end cell equals 0 row x equals 1 end table

Untuk interval 1 less than x less than 6, ambil x equals 2, maka:

open parentheses x minus 6 close parentheses open parentheses x minus 1 close parentheses equals open parentheses 2 minus 6 close parentheses open parentheses 2 minus 1 close parentheses equals negative 4 open parentheses 1 close parentheses equals negative 4 space open parentheses minus close parentheses

Garis bilangannya yaitu:

Karena pertidaksamaan bertanda "greater than" , maka daerah penyelesaian berada pada interval yang bertanda open parentheses plus close parentheses, yaitu  open curly brackets right enclose x space x less than 1 space atau space x greater than 6 comma space x element of straight real numbers close curly brackets atau open parentheses infinity minus comma space 1 close parentheses union open parentheses 6 comma space plus infinity close parentheses.

 

  • x open parentheses x minus 7 close parentheses less or equal than 8

table attributes columnalign right center left columnspacing 0px end attributes row cell x open parentheses x minus 7 close parentheses end cell less or equal than 8 row cell x squared minus 7 x end cell less or equal than 8 row cell x squared minus 7 x minus 8 end cell less or equal than 0 row cell x squared plus x minus 8 x minus 8 end cell less or equal than 0 row cell x open parentheses x plus 1 close parentheses minus 8 open parentheses x plus 1 close parentheses end cell less or equal than 0 row cell open parentheses x minus 8 close parentheses open parentheses x plus 1 close parentheses end cell less or equal than 0 end table

Pembuat nol:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x minus 8 close parentheses open parentheses x plus 1 close parentheses end cell less or equal than 0 row cell open parentheses x minus 8 close parentheses open parentheses x plus 1 close parentheses end cell equals 0 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 8 end cell equals 0 row x equals 8 end table atau table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell equals 0 row x equals cell negative 1 end cell end table

Untuk interval negative 1 less or equal than x less or equal than 8, ambil x equals 0, maka:

open parentheses x minus 8 close parentheses open parentheses x plus 1 close parentheses equals open parentheses 0 minus 8 close parentheses open parentheses 0 plus 1 close parentheses equals negative 8 open parentheses 1 close parentheses equals negative 8 space open parentheses minus close parentheses

Garis bilangannya yaitu:

Karena pertidaksamaan bertanda "less or equal than" , maka daerah penyelesaian berada pada interval yang bertanda open parentheses minus close parentheses, yaitu  open curly brackets right enclose x space minus 1 less or equal than x less or equal than 8 comma space x element of straight real numbers close curly brackets atau open square brackets negative 1 comma space 8 close square brackets.

 

Himpunan pertidakamaan dari negative 6 less than x open parentheses x minus 7 close parentheses less or equal than 8 adalah irisan dari himpunan open parentheses infinity minus comma space 1 close parentheses union open parentheses 6 comma space plus infinity close parentheses dan open square brackets negative 1 comma space 8 close square brackets.

Dengan demikian, himpunan pertidakamaan dari negative 6 less than x open parentheses x minus 7 close parentheses less or equal than 8 adalah open curly brackets right enclose x space minus 1 less or equal than x less than 1 space atau space 6 less than x less or equal than 8 close curly brackets atau open square brackets negative 1 comma space 1 close parentheses union open parentheses 6 comma space 8 close square brackets.

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