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Persamaan nilai mutlak ∣2x−1∣=7

Pertanyaan

Persamaan nilai mutlak open vertical bar 2 x minus 1 close vertical bar equals 7 

H. Firmansyah

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

diperoleh hasilnya x equals 4 atau x equals negative 3.

Pembahasan

Diperhatikan

open vertical bar 2 x minus 1 close vertical bar equals 7

Ingat 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 x greater or equal than 0 end cell row cell negative x comma space x less than 0 end cell end table close 

Diperoleh bahwa

open vertical bar 2 x minus 1 close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell 2 x minus 1 comma space 2 x minus 1 greater or equal than 0 left right double arrow x greater or equal than 1 half end cell row cell negative left parenthesis 2 x minus 1 right parenthesis comma space 2 x minus 1 less than 0 left right double arrow x less than 1 half end cell end table close 

sehingga terdapat dua kasus

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 1 end cell equals cell 7 comma space x greater or equal than 1 half end cell row cell 2 x end cell equals 8 row x equals 4 end table 

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell negative left parenthesis 2 x minus 1 right parenthesis end cell equals cell 7 comma space x less than 1 half end cell row cell negative 2 x plus 1 end cell equals 7 row cell negative 2 x end cell equals 6 row cell negative x end cell equals 3 row x equals cell negative 3 end cell end table 

Dengan demikian, diperoleh hasilnya x equals 4 atau x equals negative 3.

268

4.6 (3 rating)

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