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Sebuah pertidaksamaan nilai mutlak menghasilkan penyelesaian dalam bentuk interval . Salah satu bentuk pertidaksamaan yang sesuai dengan hasil tersebut adalah ....

Pertanyaan

Sebuah pertidaksamaan nilai mutlak menghasilkan penyelesaian dalam bentuk interval begin mathsize 14px style negative 5 less or equal than x less or equal than negative 1 end style. Salah satu bentuk pertidaksamaan yang sesuai dengan hasil tersebut adalah ....

Pembahasan Soal:

Dalam persoalan ini, terdapat beberapa jawaban antara lain seperti berikut,

begin mathsize 14px style negative 5 less or equal than x less or equal than negative 1 minus 5 plus 3 less or equal than x plus 3 less or equal than negative 1 plus 3 minus 2 less or equal than x plus 3 less or equal than 2 open vertical bar x plus 3 close vertical bar less or equal than 2 end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 30 Maret 2021

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Pertanyaan yang serupa

Tentukan penyelesaian dari pertidaksamaan !

Pembahasan Soal:

Ingat konsep syarat mutlak :

jika space open vertical bar straight x close vertical bar equals straight x space maka space straight x greater or equal than 0 jika space open vertical bar straight x close vertical bar equals negative straight x space maka space straight x less than 0 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell Syarat space 1 end cell row cell 2 x minus 6 end cell greater or equal than 0 row x greater or equal than 3 row blank blank Maka row 2 less or equal than cell 2 x minus 6 less or equal than 4 end cell row cell 2 plus 6 end cell less or equal than cell 2 x less or equal than 4 plus 6 end cell row 8 less or equal than cell 2 x less or equal than 10 end cell row 4 less or equal than cell x less or equal than 5 space left parenthesis memenuhi space syarat right parenthesis end cell row blank blank blank row blank blank cell Syarat space 2 end cell row cell negative 2 x plus 6 end cell less than 0 row x greater than 3 row blank blank Maka row 2 less or equal than cell negative 2 x plus 6 less or equal than 4 end cell row cell negative 4 end cell less or equal than cell negative 2 x less or equal than negative 2 end cell row 4 greater or equal than cell 2 x greater or equal than 2 end cell row 2 greater or equal than cell x greater or equal than 1 space left parenthesis tidak space memenuhi space syarat right parenthesis end cell row blank blank blank row blank blank cell Dengan space demikian space end cell row cell space Hp end cell equals cell 4 less or equal than straight x less or equal than 5 end cell end table  

0

Roboguru

Himpunan penyelesaian pertidaksamaan  adalah ...

Pembahasan Soal:

Sifat pertidaksamaan nilai mutlak:

"Jika open vertical bar f open parentheses x close parentheses close vertical bar less or equal than a maka negative a less or equal than f open parentheses x close parentheses less or equal than a"

Diperoleh:

table attributes columnalign right center left end attributes row space cell open vertical bar 3 x minus 7 close vertical bar end cell cell less or equal than 8 end cell row cell negative 8 less or equal than end cell cell 3 x minus 7 end cell cell less or equal than 8 end cell row cell negative 8 plus 7 less or equal than end cell cell 3 x minus 7 plus 7 end cell cell less or equal than 8 plus 7 end cell row cell negative 1 less or equal than end cell cell 3 x end cell cell less or equal than 15 end cell row cell negative 1 third less or equal than end cell cell fraction numerator 3 x over denominator 3 end fraction end cell cell less or equal than 15 over 3 end cell row cell negative 1 third less or equal than end cell x cell less or equal than 5 end cell end table

Maka, himpunan penyelesaian pertidaksamaan open vertical bar 3 x minus 7 close vertical bar less or equal than 8 adalah open curly brackets right enclose x space minus 1 third less or equal than x less or equal than 5 comma space element of straight real numbers close curly brackets.

Jadi, jawaban yang tepat adalah A.

0

Roboguru

Semua nilai  yang memenuhi pertidaksamaan  adalah ...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row 0 less than cell open vertical bar x minus 3 close vertical bar less or equal than 3 end cell row 0 less than cell open vertical bar x minus 3 close vertical bar space dan space open vertical bar x minus 3 close vertical bar less or equal than 3 end cell row cell open vertical bar x minus 3 close vertical bar space end cell greater than cell 0 space dan space open vertical bar x minus 3 close vertical bar less or equal than 3 end cell row x not equal to cell 3 space dan space minus 3 less or equal than x minus 3 less or equal than 3 end cell row x not equal to cell 3 space dan space minus 3 plus 3 less or equal than x minus 3 plus 3 less or equal than 3 plus 3 end cell row x not equal to cell 3 space dan space 0 less or equal than x less or equal than 6 end cell row 0 less or equal than cell x less than 3 space atau space 3 less than x less or equal than 6 end cell end table

Jadi, jawaban yang tepat adalah B

0

Roboguru

Semua nilai  yang memenuhi pertidaksamaan  adalah...

Pembahasan Soal:

Diketahui pertidaksamaan 0 less than open vertical bar x minus 3 close vertical bar less or equal than 3, maka 0 less than x minus 3 less or equal than 3 atau negative 3 less or equal than x minus 3 less than 0. Ketika 0 less than x minus 3 less or equal than 3, nilai x yang memenuhi sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row 0 less than cell x minus 3 less or equal than 3 end cell row cell 0 plus 3 end cell less than cell x minus 3 plus 3 less or equal than 3 plus 3 end cell row 3 less than cell x less or equal than 6 end cell end table

Ketika negative 3 less or equal than x minus 3 less than 0, nilai x yang memenuhi sebagai berikut.

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

Berdasarkan uraian di atas, semua nilai x yang memenuhi pertidaksamaan 0 less than open vertical bar x minus 3 close vertical bar less or equal than 3 adalah 0 less or equal than x less than 3 atau 3 less than x less or equal than 6.

Oleh karena itu, jawaban yang benar adalah B.

3

Roboguru

Which of the following is equivalent to ?

Pembahasan Soal:

Diketahui pertidaksamaan 1 less or equal than open vertical bar x minus 2 close vertical bar less or equal than 4, maka 1 less or equal than x minus 2 less or equal than 4 atau negative 4 less or equal than x minus 2 less or equal than negative 1. Ketika 1 less or equal than x minus 2 less or equal than 4, nilai x yang memenuhi sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row 1 less or equal than cell x minus 2 less or equal than 4 end cell row cell 1 plus 2 end cell less or equal than cell x minus 2 plus 2 less or equal than 4 plus 2 end cell row 3 less or equal than cell x less or equal than 6 end cell end table

Kemudian, ketika negative 4 less or equal than x minus 2 less or equal than negative 1, nilai x yang memenuhi sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 4 end cell less or equal than cell x minus 2 less or equal than negative 1 end cell row cell negative 4 plus 2 end cell less or equal than cell x minus 2 plus 2 less or equal than negative 1 plus 2 end cell row cell negative 2 end cell less or equal than cell x less or equal than 1 end cell end table

Berdasarkan uraian di atas, maka pertidaksamaan 1 less or equal than open vertical bar x minus 2 close vertical bar less or equal than 4 ekuivalen dengan negative 2 less or equal than x less or equal than 1 atau 3 less or equal than x less or equal than 6.

Oleh karena itu, jawaban yang benar adalah E.

0

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