∣x+5∣=5, berapakah nilai x?

Pertanyaan

open vertical bar x plus 5 close vertical bar equals 5 comma berapakah nilai x?

R. Bella

Master Teacher

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

Jawaban terverifikasi

Jawaban

nilai x adalah x equals negative 10 space logical or space x equals 0.  

Pembahasan

Ingat sifat persamaan nilai mutlak:

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

Sehingga diperoleh:

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

Untuk x greater or equal than negative 5

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

Untuk x less than negative 5

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x plus 5 close vertical bar end cell equals 5 row cell x plus 5 end cell equals cell negative 5 end cell row x equals cell negative 10 end cell end table

Jadi, nilai x adalah x equals negative 10 space logical or space x equals 0.  

98

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