Selesaikan dan tuliskan himpunan penyelesaiannya dari PtNM berikut. d. ∣∣​2x−15​∣∣​≥∣∣​x−21​∣∣​

Pertanyaan

Selesaikan dan tuliskan himpunan penyelesaiannya dari PtNM berikut.

d. open vertical bar fraction numerator 5 over denominator 2 x minus 1 end fraction close vertical bar greater or equal than open vertical bar fraction numerator 1 over denominator x minus 2 end fraction close vertical bar 

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

himpunan penyelesaian pertidaksamaan open vertical bar fraction numerator 5 over denominator 2 x minus 1 end fraction close vertical bar greater or equal than open vertical bar fraction numerator 1 over denominator x minus 2 end fraction close vertical bar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets right enclose x x less or equal than 11 over 7 space atau space x greater or equal than 3 comma space x not equal to 1 half close curly brackets end cell end table

Pembahasan

Syarat:

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

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

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 5 over denominator 2 x minus 1 end fraction close vertical bar end cell greater or equal than cell open vertical bar fraction numerator 1 over denominator x minus 2 end fraction close vertical bar end cell row cell fraction numerator open vertical bar 5 close vertical bar over denominator open vertical bar 2 x minus 1 close vertical bar end fraction end cell greater or equal than cell fraction numerator open vertical bar 1 close vertical bar over denominator open vertical bar x minus 2 close vertical bar end fraction end cell row cell fraction numerator 5 over denominator open vertical bar 2 x minus 1 close vertical bar end fraction end cell greater or equal than cell fraction numerator 1 over denominator open vertical bar x minus 2 close vertical bar end fraction end cell row cell 5 open vertical bar x minus 2 close vertical bar end cell greater or equal than cell open vertical bar 2 x minus 1 close vertical bar end cell row cell open vertical bar 5 x minus 10 close vertical bar end cell greater or equal than cell open vertical bar 2 x minus 1 close vertical bar end cell row cell left parenthesis left parenthesis 5 x minus 10 right parenthesis plus left parenthesis 2 x minus 1 right parenthesis right parenthesis left parenthesis left parenthesis 5 x minus 10 right parenthesis minus left parenthesis 2 x minus 1 right parenthesis right parenthesis end cell greater or equal than 0 row cell left parenthesis 5 x minus 10 plus 2 x minus 1 right parenthesis left parenthesis 5 x minus 10 minus 2 x plus 1 right parenthesis end cell greater or equal than 0 row cell left parenthesis 7 x minus 11 right parenthesis left parenthesis 3 x minus 9 right parenthesis end cell greater or equal 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 or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 11 over 7 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 or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 9 over 3 end cell 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 or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 11 over 7 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 or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 space...... space left parenthesis 3 right parenthesis end cell end table 

Iriskan (1), (2) dan (3) sehingga penyelesaiannya menjadi 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 or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 11 over 7 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 or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell 3 comma space x end cell not equal to cell 1 half end cell end table.

Jadi, himpunan penyelesaian pertidaksamaan open vertical bar fraction numerator 5 over denominator 2 x minus 1 end fraction close vertical bar greater or equal than open vertical bar fraction numerator 1 over denominator x minus 2 end fraction close vertical bar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets right enclose x x less or equal than 11 over 7 space atau space x greater or equal than 3 comma space x not equal to 1 half close curly brackets end cell end table

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Selesaikan dan tuliskan himpunan penyelesaiannya dari PtNM berikut. b. ∣∣​3+x6−5x​∣∣​​≤​21​​

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