Pertanyaan

Selesaikan dan tuliskan himpunan penyelesaiannya dari PtNM berikut. d. ∣ ∣ 2 x − 1 5 ∣ ∣ ≥ ∣ ∣ x − 2 1 ∣ ∣

Selesaikan dan tuliskan himpunan penyelesaiannya dari PtNM berikut.

d. $∣ ∣ \frac{5}{2 x - 1} ∣ ∣ \geq ∣ ∣ \frac{1}{x - 2} ∣ ∣$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

himpunan penyelesaian pertidaksamaan adalah

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

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: Sehingga: Iriskan (1), (2) dan (3) sehingga penyelesaiannya menjadi . Jadi, himpunan penyelesaian pertidaksamaan adalah

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:

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

Iriskan (1), (2) dan (3) sehingga penyelesaiannya menjadi .

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