Pertanyaan

Selesaikan setiap pertidaksamaan berikut. d. ∣ x + 1 ∣ 2 − 5 ∣ x + 1 ∣ + 4 < 0

Selesaikan setiap pertidaksamaan berikut.

d. $∣ x + 1 ∣^{2} - 5 ∣ x + 1 ∣ + 4 < 0$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

penyelesaian pertidaksamaan adalah

penyelesaian pertidaksamaan open vertical bar x plus 1 close vertical bar squared minus 5 open vertical bar x plus 1 close vertical bar plus 4 less than 0

open vertical bar x plus 1 close vertical bar squared minus 5 open vertical bar x plus 1 close vertical bar plus 4 less than 0

adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank less than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank less than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table table attributes columnalign right center left columnspacing 0px end attributes row blank less than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank less than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table

Pembahasan

Misalkan , maka: Ingat, , sehingga: Jadi, penyelesaian pertidaksamaan adalah

Misalkan open vertical bar x plus 1 close vertical bar equals p , maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell p squared minus 5 p plus 4 end cell less than 0 row cell left parenthesis p minus 1 right parenthesis left parenthesis p minus 4 right parenthesis end cell less than 0 end table

1 less than p less than 4

Ingat, p equals open vertical bar x plus 1 close vertical bar , sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row x less than cell negative 2 space atau space x greater than 0 space dan space minus 5 less than x less than 3 end cell row cell negative 5 end cell less than cell x less than negative 2 space atau space 0 less than x less than 3 end cell end table

Jadi, penyelesaian pertidaksamaan adalah