Pertanyaan

Tentukanlah HP ∣ x + 1 ∣ = ∣ x − 4 ∣

Tentukanlah HP $∣ x + 1 ∣ = ∣ x - 4 ∣$

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari adalah .

himpunan penyelesaian dari open vertical bar x plus 1 close vertical bar equals open vertical bar x minus 4 close vertical bar

adalah

Pembahasan

Ingatlah aturan nilai mutlak! Maka, a. atau b. atau Di dapatkan interval , , dan . Untuk interval Untuk interval , Di dapatkan dan . Untuk interval Jadi, himpunan penyelesaian dari adalah .

Ingatlah 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 plus 1 close vertical bar

open vertical bar x plus 1 close vertical bar equals x plus 1

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell greater or equal than cell thin space 0 end cell row cell x plus 1 minus 1 end cell greater or equal than cell thin space 0 minus 1 end cell row x greater or equal than cell thin space minus 1 end cell end table

atau

open vertical bar x plus 1 close vertical bar equals negative open parentheses x plus 1 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell less than 0 row cell x plus 1 minus 1 end cell less than cell 0 minus 1 end cell row x less than cell negative 1 end cell end table

b. open vertical bar x minus 4 close vertical bar

open vertical bar x minus 4 close vertical bar equals x minus 4

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 4 end cell greater or equal than cell thin space 0 end cell row cell x minus 4 plus 4 end cell greater or equal than cell thin space 0 plus 4 end cell row x greater or equal than cell thin space 4 end cell end table

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 4 end cell less than 0 row cell x minus 4 plus 4 end cell less than cell 0 plus 4 end cell row x less than 4 end table

Di dapatkan interval x less than negative 1 , negative 1 less or equal than thin space x less than 4 , dan x greater or equal than thin space 4 .

Untuk interval x less than negative 1

Untuk interval negative 1 less or equal than thin space x less than 4 ,

$table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell equals cell negative open parentheses x minus 4 close parentheses end cell row cell x plus 1 end cell equals cell negative x plus 4 end cell row cell x plus 1 minus 1 end cell equals cell negative x plus 4 minus 1 end cell row x equals cell negative x plus 3 end cell row cell x plus x end cell equals cell negative x plus 3 plus x end cell row cell 2 x end cell equals 3 row cell fraction numerator 2 x over denominator 2 end fraction end cell equals cell 3 over 2 end cell row x equals cell 3 over 2 end cell row blank blank blank end table$

Di dapatkan negative 1 less or equal than thin space x less than 4 dan x equals 3 over 2 .

Untuk interval x greater or equal than thin space 4

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell equals cell x minus 4 end cell row cell x plus 1 minus x end cell equals cell x minus 4 minus x end cell row 1 equals cell negative 4 open parentheses tidak space memenuhi close parentheses end cell end table

Jadi, himpunan penyelesaian dari open vertical bar x plus 1 close vertical bar equals open vertical bar x minus 4 close vertical bar adalah x equals 3 over 2 .