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Tentukan himpunan penyelesaian dari vertical line x minus 5 vertical line plus vertical line 3 x minus 1 vertical line equals 12

D. Nuryani

Master Teacher

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari persamaan nilai mutlak di atas adalah x equals open curly brackets negative 3 over 2 comma space 4 close curly brackets.

Pembahasan

Definisi nilai mutlak:

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

Penyelesaian:

Berdasarkan definisi nilai mutlak, maka jabarkan terlebih dahulu setiap nilai mutlak dalam persamaan.

vertical line x minus 5 vertical line plus vertical line 3 x minus 1 vertical line equals 12,

open vertical bar x minus 5 close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell x minus 5 comma space untuk space x greater or equal than 5 end cell row cell negative open parentheses x minus 5 close parentheses comma space untuk space x less than 5 end cell end table close

open vertical bar 3 x minus 1 close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell 3 x minus 1 comma space untuk space x greater or equal than 1 third end cell row cell negative open parentheses 3 x minus 1 close parentheses comma space untuk space x less than 1 third end cell end table close

  • Solusi pada interval negative infinity less than x less than 1 third

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line x minus 5 vertical line plus vertical line 3 x minus 1 vertical line end cell equals 12 row cell negative open parentheses x minus 5 close parentheses minus open parentheses 3 x minus 1 close parentheses end cell equals 12 row cell negative x plus 5 minus 3 x plus 1 end cell equals 12 row cell negative 4 x plus 6 end cell equals 12 row cell negative 4 x end cell equals cell 12 minus 6 end cell row cell negative 4 x end cell equals 6 row x equals cell negative 6 over 4 end cell row x equals cell negative 3 over 2 space left parenthesis memenuhi right parenthesis end cell end table 

  • Solusi pada interval 1 third less or equal than x less than 5

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line x minus 5 vertical line plus vertical line 3 x minus 1 vertical line end cell equals 12 row cell negative open parentheses x minus 5 close parentheses plus 3 x minus 1 end cell equals 12 row cell negative x plus 5 plus 3 x minus 1 end cell equals 12 row cell 2 x plus 4 end cell equals 12 row cell 2 x end cell equals cell 12 minus 4 end cell row cell 2 x end cell equals 8 row x equals cell 8 over 2 end cell row x equals cell 4 space left parenthesis memenuhi right parenthesis end cell end table

  • Solusi pada interval 5 less or equal than x less than infinity

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line x minus 5 vertical line plus vertical line 3 x minus 1 vertical line end cell equals 12 row cell x minus 5 plus 3 x minus 1 end cell equals 12 row cell 4 x minus 6 end cell equals 12 row cell 4 x end cell equals cell 12 plus 6 end cell row cell 4 x end cell equals 18 row x equals cell 18 over 4 end cell row x equals cell 9 over 2 space left parenthesis tidak space memenuhi right parenthesis end cell end table

Dengan demikian, himpunan penyelesaian dari persamaan nilai mutlak di atas adalah x equals open curly brackets negative 3 over 2 comma space 4 close curly brackets.

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