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Pertanyaan

Tentukan himpunan penyelesaian dari open vertical bar x minus 4 close vertical bar plus open vertical bar x close vertical bar equals 8.

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Definisi nilai mutlak: 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

Penyelesaian:

open vertical bar x minus 4 close vertical bar plus open vertical bar x close vertical bar equals 8, berdasarkan definisi maka:

open vertical bar x minus 4 close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell x minus 4 comma space untuk space x greater or equal than 4 end cell row cell negative left parenthesis x minus 4 right parenthesis comma space untuk space x less than 4 end cell end table close 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

  • Solusi pada interval negative infinity less than x less than 0

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 x close vertical bar end cell equals 8 row cell negative left parenthesis x minus 4 right parenthesis plus left parenthesis negative x right parenthesis end cell equals 8 row cell negative x plus 4 minus x end cell equals 8 row cell negative 2 x end cell equals cell 8 minus 4 end cell row cell negative 2 x end cell equals 4 row x equals cell negative 4 over 2 end cell row x equals cell negative 2 space left parenthesis memenuhi right parenthesis end cell end table

  •   Solusi pada interval 0 less or equal than x less than 4

 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 x close vertical bar end cell equals 8 row cell negative left parenthesis x minus 4 right parenthesis plus x end cell equals 8 row cell negative x plus 4 plus x end cell equals 8 row 0 equals cell 8 minus 4 end cell row 0 equals cell 4 space left parenthesis salah divided by tidak space memenuhi right parenthesis end cell row blank blank blank end table

  • Solusi pada interval 4 less or equal than x less than infinity

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 x close vertical bar end cell equals 8 row cell x minus 4 plus x end cell equals 8 row cell 2 x end cell equals cell 8 plus 4 end cell row cell 2 x end cell equals 12 row x equals cell 12 over 2 end cell row x equals cell 6 space left parenthesis memenuhi right parenthesis end cell end table

Dengan demikian, himpunan penyelesaian persamaan nilai mutlak di atas adalah x equals open curly brackets negative 2 comma space 6 close curly brackets.

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