Interval nilai x yang memenuhi pertidaksamaan ∣∣​x2−6x−4∣∣​>12 adalah ...

Pertanyaan

Interval nilai x yang memenuhi pertidaksamaan open vertical bar x squared minus 6 x minus 4 close vertical bar greater than 12 adalah ...space space

  1. 2 less than x less than 4space space

  2. x less than negative 2 space atau space x greater than 8space space

  3. negative 2 less than x less than 2 space atau space 4 less than x less than 8space space

  4. x less than negative 2 space atau space 2 less than x less than 4 space atau space x greater than 8space space

  5. tidak ada nilai x yang memenuhispace space

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat sifat pertidaksamaan nilai mutlak berikut,

open vertical bar f left parenthesis x right parenthesis close vertical bar greater than a comma space maka space f left parenthesis x right parenthesis less than a space d a n space f left parenthesis x right parenthesis greater than a

Diketahui :

  • open vertical bar x squared minus 6 x minus 4 close vertical bar greater than 12

Ditanya : Interval x yang memenuhi pertidaksamaan.

Jawab :

open vertical bar f left parenthesis x right parenthesis close vertical bar greater than a comma space maka space f left parenthesis x right parenthesis less than negative a space d a n space f left parenthesis x right parenthesis greater than a

  • f left parenthesis x right parenthesis less than negative a

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 6 x minus 4 end cell less than cell negative 12 end cell row cell x squared minus 6 x minus 4 plus 12 end cell less than 0 row cell x squared minus 6 x plus 8 end cell less than 0 row cell x squared minus 6 x plus 8 end cell equals 0 row cell open parentheses x minus 4 close parentheses left parenthesis x minus 2 right parenthesis end cell equals 0 row x equals cell 4 space a t a u space x equals space 2 end cell row blank blank blank end table

  • italic f left parenthesis italic x right parenthesis greater than italic a

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 6 x minus 4 end cell greater than 12 row cell x squared minus 6 x minus 4 minus 12 end cell greater than 0 row cell x squared minus 6 x minus 16 end cell greater than 0 row cell x squared minus 6 x minus 16 end cell equals 0 row cell open parentheses x minus 8 close parentheses left parenthesis x plus 2 right parenthesis end cell equals 0 row x equals cell 8 space a t a u space x equals space minus 2 end cell row blank blank blank end table

Sehingga jika dimasukkan dalam garis bilangan sebagai berikut

atau

x less than negative 2 space atau space 2 less than x less than 4 space atau space x greater than 8

Oleh karena itu, jawaban yang benar adalah D.

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