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Tentukan Himpunan Penyelesaian dari: 1. ∣x+1∣+∣x+3∣=6

Pertanyaan

Tentukan Himpunan Penyelesaian dari:

1. open vertical bar x plus 1 close vertical bar plus open vertical bar x plus 3 close vertical bar equals 6 

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari open vertical bar x plus 1 close vertical bar plus open vertical bar x plus 3 close vertical bar equals 6 adalah open curly brackets 1 close curly brackets.

Pembahasan

Ingat kembali:

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

Penyelesaian dari open vertical bar x plus 1 close vertical bar plus open vertical bar x plus 3 close vertical bar equals 6 dapat ditentukan sebagai berikut:

  • Untuk x greater or equal than 0 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x plus 1 close vertical bar plus open vertical bar x plus 3 close vertical bar end cell equals 6 row cell open parentheses x plus 1 close parentheses plus open parentheses x plus 3 close parentheses end cell equals 6 row cell x plus 1 plus x plus 3 end cell equals 6 row cell 2 x plus 4 end cell equals 6 row cell 2 x end cell equals cell 6 minus 4 end cell row cell 2 x end cell equals 2 row x equals cell 2 over 2 end cell row x equals 1 end table 

  • Untuk x less than 0 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x plus 1 close vertical bar plus open vertical bar x plus 3 close vertical bar end cell equals 6 row cell open parentheses x plus 1 close parentheses plus open parentheses negative open parentheses x plus 3 close parentheses close parentheses end cell equals 6 row cell up diagonal strike x plus 1 up diagonal strike negative x end strike minus 3 end cell equals cell 6 rightwards arrow tidak space ada space penyelesaian end cell end table 

Jadi, himpunan penyelesaian dari open vertical bar x plus 1 close vertical bar plus open vertical bar x plus 3 close vertical bar equals 6 adalah open curly brackets 1 close curly brackets.

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