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Pertanyaan

Sederhanakan bentuk berikut.

b. open vertical bar x minus 4 close vertical bar plus open vertical bar 2 minus x close vertical bar plus open vertical bar 2 x minus 1 close vertical bar space jika space x greater than 4          

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

bentuk sederhana dari open vertical bar x minus 4 close vertical bar plus open vertical bar 2 minus x close vertical bar plus open vertical bar 2 x minus 1 close vertical bar space jika space x greater than 4 adalah 4 x minus 7.

Pembahasan

Ingat kembali definisi mutlak berikut!

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

Jika x greater than 4, maka nilai x minus 4 greater than 0.

Berdasarkan definisi mutlak di atas, maka

 table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x minus 4 close vertical bar end cell equals cell x minus 4 end cell end table 

Jika x greater than 4, maka nilai 2 minus x less than 0.

Berdasarkan definisi mutlak di atas, maka

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

Jika x greater than 4, maka nilai 2 x minus 1 greater than 0.

Berdasarkan definisi mutlak di atas, maka

 table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 x minus 1 close vertical bar end cell equals cell 2 x minus 1 end cell end table 

Sehingga  open vertical bar x minus 4 close vertical bar plus open vertical bar 2 minus x close vertical bar plus open vertical bar 2 x minus 1 close vertical bar dapat disederhanakan menjadi

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x minus 4 close vertical bar plus open vertical bar 2 minus x close vertical bar plus open vertical bar 2 x minus 1 close vertical bar end cell equals cell left parenthesis x minus 4 right parenthesis plus left parenthesis negative 2 plus x right parenthesis plus left parenthesis 2 x minus 1 right parenthesis end cell row blank equals cell x plus x plus 2 x plus negative 4 minus 2 minus 1 end cell row blank equals cell 4 x minus 7 end cell end table  .

Jadi, bentuk sederhana dari open vertical bar x minus 4 close vertical bar plus open vertical bar 2 minus x close vertical bar plus open vertical bar 2 x minus 1 close vertical bar space jika space x greater than 4 adalah 4 x minus 7.

83

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