Pertanyaan

Tentukan himpunan penyelesaian dari setiap PtNM berikut. c. ∣ x − 1 ∣ ∣ x − 2 ∣ + 3 − 1 < 0

Tentukan himpunan penyelesaian dari setiap PtNM berikut.

c. $\frac{∣ x - 2 ∣ + 3}{∣ x - 1 ∣} - 1 < 0$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

himpunan penyelesaian pertidaksamaan adalah

himpunan penyelesaian pertidaksamaan $fraction numerator open vertical bar x minus 2 close vertical bar plus 3 over denominator open vertical bar x minus 1 close vertical bar end fraction minus 1 less than 0$ adalah

open curly brackets table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell right enclose x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table table attributes columnalign right center left columnspacing 0px end attributes row blank less than blank end table table attributes columnalign right center left columnspacing 0px end attributes row x less than cell 3 over 2 end cell end table comma space x not equal to 1 close curly brackets

Pembahasan

Syarat: Maka: Iriskan (1) dan (2) sehingga penyelesaiannya menjadi . Jadi, himpunan penyelesaian pertidaksamaan adalah

Syarat:

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 1 end cell not equal to 0 row x not equal to cell 1 space..... space left parenthesis 1 right parenthesis end cell end table

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open vertical bar x minus 2 close vertical bar plus 3 over denominator open vertical bar x minus 1 close vertical bar end fraction minus 1 end cell less than 0 row cell fraction numerator open vertical bar x minus 2 close vertical bar plus 3 minus open vertical bar x minus 1 close vertical bar over denominator open vertical bar x minus 1 close vertical bar end fraction end cell less than 0 row cell open vertical bar x minus 2 close vertical bar plus 3 minus open vertical bar x minus 1 close vertical bar end cell less than 0 row cell open vertical bar x minus 2 close vertical bar end cell less than cell open vertical bar x minus 1 close vertical bar minus 3 end cell row cell open vertical bar x minus 2 close vertical bar squared end cell less than cell open parentheses open vertical bar x minus 1 close vertical bar minus 3 close parentheses squared end cell end table$

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Iriskan (1) dan (2) sehingga penyelesaiannya menjadi table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table table attributes columnalign right center left columnspacing 0px end attributes row blank less than blank end table table attributes columnalign right center left columnspacing 0px end attributes row x less than cell 3 over 2 end cell end table comma x not equal to 1 .

Jadi, himpunan penyelesaian pertidaksamaan $fraction numerator open vertical bar x minus 2 close vertical bar plus 3 over denominator open vertical bar x minus 1 close vertical bar end fraction minus 1 less than 0$ adalah