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Tentukan himpunan penyelesaiannya! 3. ∣x∣+∣x+3∣=5

Pertanyaan

Tentukan himpunan penyelesaiannya!

3. open vertical bar x close vertical bar plus open vertical bar x plus 3 close vertical bar equals 5

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari open vertical bar x close vertical bar plus open vertical bar x plus 3 close vertical bar equals 5 adalah x equals 1 atau x equals negative 4.

Pembahasan

Ingat aturan nilai mutlak!

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

Maka,

a. open vertical bar x close vertical bar

open vertical bar x close vertical bar equals x

atau

open vertical bar x close vertical bar equals negative x

b. table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x plus 3 close vertical bar end cell equals cell x plus 3 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 3 end cell greater or equal than cell thin space 0 end cell row cell x plus 3 minus 3 end cell greater or equal than cell thin space 0 minus 3 end cell row x greater or equal than cell thin space minus 3 end cell end table

atau

open vertical bar x plus 3 close vertical bar equals negative open parentheses x plus 3 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 3 end cell less than 0 row cell x plus 3 minus 3 end cell less than cell 0 minus 3 end cell row x less than cell negative 3 end cell end table

Untuk x less than negative 3,

 table attributes columnalign right center left columnspacing 0px end attributes row cell negative x minus open parentheses x plus 3 close parentheses end cell equals 5 row cell negative x minus x minus 3 end cell equals 5 row cell negative 2 x end cell equals cell 5 plus 3 end cell row cell negative 2 x end cell equals 8 row x equals cell fraction numerator 8 over denominator negative 2 end fraction end cell row x equals cell negative 4 end cell end table

Di dapatkan x less than negative 3 dan x equals negative 4.

Untuk x greater or equal than 0 dengan x equals 1,

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus x plus 3 end cell equals 5 row cell 2 x plus 3 end cell equals 5 row cell 2 x plus 3 minus 3 end cell equals cell 5 minus 3 end cell row cell 2 x end cell equals 2 row cell fraction numerator 2 x over denominator 2 end fraction end cell equals cell 2 over 2 end cell row x equals 1 row blank blank blank end table

Di dapatkan x equals 1 atau x greater or equal than 0.


Jadi, himpunan penyelesaian dari open vertical bar x close vertical bar plus open vertical bar x plus 3 close vertical bar equals 5 adalah x equals 1 atau x equals negative 4.

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