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Selesaikan setiap pertidaksamaan berikut. c. ∣ x − 3 ∣ 2 − 4 ∣ x − 3 ∣ − 5 ≤ 0

Selesaikan setiap pertidaksamaan berikut.

c.  

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

penyelesaian dari pertidaksamaan adalah

penyelesaian dari pertidaksamaan open vertical bar x minus 3 close vertical bar squared minus 4 open vertical bar x minus 3 close vertical bar minus 5 less or equal 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank less or equal 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 or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table 

Pembahasan

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

Misalkan open vertical bar x minus 3 close vertical bar equals p, maka:

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

negative 1 table attributes columnalign right center left columnspacing 0px end attributes row blank less or equal than blank end table p table attributes columnalign right center left columnspacing 0px end attributes row blank less or equal than blank end table 5

Ingat, p equals open vertical bar x minus 3 close vertical bar

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 1 end cell less or equal than cell open vertical bar x minus 3 close vertical bar less or equal than 5 end cell row cell negative 1 end cell less or equal than cell open vertical bar x minus 3 space close vertical bar space dan space open vertical bar x minus 3 close vertical bar less or equal than 5 end cell row cell open vertical bar x minus 3 close vertical bar end cell greater or equal than cell negative 1 space dan space open vertical bar x minus 3 close vertical bar less or equal than 5 end cell row cell negative infinity end cell less or equal than cell x less or equal than infinity space dan space minus 5 less or equal than x minus 3 less or equal than 5 end cell row cell negative infinity end cell less or equal than cell x less or equal than infinity space dan space minus 5 plus 3 less or equal than x minus 3 plus 3 less or equal than 5 plus 3 end cell row cell negative infinity end cell less or equal than cell x less or equal than infinity space dan space minus 2 less or equal than x less or equal than 8 end cell row cell negative 2 end cell less or equal than cell x less or equal than 8 end cell end table 

Jadi, penyelesaian dari pertidaksamaan open vertical bar x minus 3 close vertical bar squared minus 4 open vertical bar x minus 3 close vertical bar minus 5 less or equal 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank less or equal 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 or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table 

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