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Selesaikan dan tuliskan himpunan penyelesaiannya dari PtNM berikut. c. ∣ ∣ ​ 2 x − 3 x + 2 ​ ∣ ∣ ​ < 4

Selesaikan dan tuliskan himpunan penyelesaiannya dari PtNM berikut.

c.  

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

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himpunan penyelesaian dari adalah

himpunan penyelesaian dari open vertical bar fraction numerator x plus 2 over denominator 2 x minus 3 end fraction close vertical bar less than 4 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets right enclose x x less than 10 over 9 space atau space x greater than 2 close curly brackets end cell end table 

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Pembahasan

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

Syarat:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 3 end cell not equal to 0 row cell 2 x end cell not equal to 3 row x not equal to cell 3 over 2 space... space left parenthesis 1 right parenthesis end cell end table

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator x plus 2 over denominator 2 x minus 3 end fraction close vertical bar end cell less than 4 row cell fraction numerator open vertical bar x plus 2 close vertical bar over denominator open vertical bar 2 x minus 3 close vertical bar end fraction end cell less than 4 row cell open vertical bar x plus 2 close vertical bar end cell less than cell 4 open vertical bar 2 x minus 3 close vertical bar end cell row cell open vertical bar x plus 2 close vertical bar end cell less than cell open vertical bar 8 x minus 12 close vertical bar end cell row cell left parenthesis left parenthesis x plus 2 right parenthesis plus left parenthesis 8 x minus 12 right parenthesis right parenthesis left parenthesis left parenthesis x plus 2 right parenthesis minus left parenthesis 8 x minus 12 right parenthesis right parenthesis end cell less than 0 row cell left parenthesis x plus 2 plus 8 x minus 12 right parenthesis left parenthesis x plus 2 minus 8 x plus 12 right parenthesis end cell less than 0 row cell left parenthesis 9 x minus 10 right parenthesis left parenthesis negative 7 x plus 14 right parenthesis end cell less than 0 end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 blank blank cell 10 over 9 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank greater than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 14 over 7 end cell end table x 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 blank blank cell 10 over 9 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank greater than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table space... space left parenthesis 2 right parenthesis

Iriskan (1) dan (2) sehingga penyelesaiannya menjadi x 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 blank blank cell 10 over 9 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank greater than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table.

Jadi, himpunan penyelesaian dari open vertical bar fraction numerator x plus 2 over denominator 2 x minus 3 end fraction close vertical bar less than 4 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets right enclose x x less than 10 over 9 space atau space x greater than 2 close curly brackets end cell end table 

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Nilai x yang memenuhi pertidaksamaan ∣ ∣ ​ x + 2 x − 3 ​ ∣ ∣ ​ < 4 adalah ....

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