Tantukan ∣−2x+5∣ untuk x bilangan real dengan menggunakan defenisi nilai mutlak.

Pertanyaan

Tantukan open vertical bar negative 2 x plus 5 close vertical bar untuk x bilangan real dengan menggunakan defenisi nilai mutlak.

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

dengan menggunakan definisi dari open vertical bar negative 2 x plus 5 close vertical bar adalah begin mathsize 12px style open vertical bar table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 2 x plus 5 end cell end table close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell 2 x minus 5 comma space untuk space x greater than 5 over 2 end cell row cell 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 x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table space space untuk space x less or equal than 5 over 2 end cell end table close end style 

Pembahasan

Ingat kembali dari definisi nilai mutlak:

open vertical bar x close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell negative x comma space x less than 0 end cell row cell x comma space x greater or equal than 0 end cell end table close

Sehingga diperoleh perhitungan: 

-solusi pertama:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar negative 2 x plus 5 close vertical bar end cell equals cell negative open parentheses negative 2 x plus 5 close parentheses end cell row blank equals cell 2 x minus 5 end cell end table 

Untuk

table attributes columnalign right center left columnspacing 0px end attributes row cell size 12px minus size 12px 2 size 12px x size 12px plus size 12px 5 end cell size 12px less than size 12px 0 row cell size 12px minus size 12px 2 size 12px x end cell size 12px less than cell size 12px minus size 12px 5 size 12px space begin mathsize 12px style left parenthesis d i k a l i space left parenthesis negative right parenthesis right parenthesis end style end cell row cell 2 size 12px x end cell size 12px greater than size 12px 5 row size 12px x size 12px greater than cell 5 over 2 end cell end table

-solusi kedua:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar negative 2 x plus 5 close vertical bar end cell equals cell negative 2 x plus 5 end cell end table 

Untuk

table attributes columnalign right center left columnspacing 0px end attributes row cell size 12px minus size 12px 2 size 12px x size 12px plus size 12px 5 end cell size 12px greater or equal than size 12px 0 row cell size 12px minus size 12px 2 size 12px x end cell size 12px greater or equal than cell size 12px minus size 12px 5 size 12px space begin mathsize 12px style left parenthesis d i k a l i space left parenthesis negative right parenthesis right parenthesis end style end cell row cell 2 size 12px x end cell size 12px less or equal than size 12px 5 row size 12px x size 12px less or equal than cell 5 over 2 end cell end table

Jadi, dengan menggunakan definisi dari open vertical bar negative 2 x plus 5 close vertical bar adalah begin mathsize 12px style open vertical bar table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 2 x plus 5 end cell end table close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell 2 x minus 5 comma space untuk space x greater than 5 over 2 end cell row cell 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 x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table space space untuk space x less or equal than 5 over 2 end cell end table close end style 

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