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Bentuk x 2 − 3 x + 2 3 < x 2 − 4 x + 3 5 benar untuk ...

Bentuk $\frac{3}{x ^{2} - 3 x + 2} < \frac{5}{x ^{2} - 4 x + 3}$ benar untuk ...

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Jawaban terverifikasi

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Nilai x yang memenuhi adalah Buat garis bilangan untuk nilai x yang memenuhi, sehingga : Uji masing-masing daerah menjadi : Maka garis bilangan menjadi : Karena pertidaksamaan berbentuk “kurang dari” maka daerah yang dipilih adalah daerah negatif sehingga diperoleh penyelesaian: . Kemudian sesuai dengan opsi pada pilihan jawaban maka dipilih

Nilai x yang memenuhi adalah

$fraction numerator 3 over denominator straight x squared minus 3 straight x plus 2 end fraction less than fraction numerator 5 over denominator straight x squared minus 4 straight x plus 3 end fraction fraction numerator 3 over denominator left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 1 right parenthesis end fraction minus fraction numerator 5 over denominator left parenthesis straight x minus 3 right parenthesis left parenthesis straight x minus 1 right parenthesis end fraction less than 0 fraction numerator 3 straight x minus 9 minus left parenthesis 5 straight x minus 10 right parenthesis over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction less than 0 fraction numerator 2 straight x plus 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction less than 0 straight x equals 1 half semicolon space straight x equals 1 semicolon space straight x equals 2 space dan space straight x equals 3 straight x not equal to 1 semicolon space straight x not equal to 1 space dan space straight x not equal to 3$

Buat garis bilangan untuk nilai x yang memenuhi, sehingga :

Uji masing-masing daerah menjadi :

$Untuk space straight x less than 1 half comma space pilih space straight x equals negative 1 space menjadi fraction numerator negative 2 straight x plus 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction equals fraction numerator negative 2 left parenthesis negative space 1 right parenthesis plus 1 over denominator left parenthesis left parenthesis negative 1 right parenthesis minus 1 right parenthesis left parenthesis left parenthesis negative 1 right parenthesis minus 2 right parenthesis left parenthesis left parenthesis negative 1 right parenthesis minus 3 right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 plus 1 over denominator left parenthesis negative 2 right parenthesis left parenthesis negative 3 right parenthesis left parenthesis negative 4 right parenthesis end fraction equals negative 2 over 24 space left parenthesis negatif right parenthesis Untuk space 1 half less than straight x less than 1 comma space pilih space straight x equals 3 over 4 space menjadi fraction numerator negative 2 straight x plus 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction equals fraction numerator negative 2 left parenthesis begin display style 3 over 4 end style right parenthesis plus 1 over denominator left parenthesis left parenthesis begin display style 3 over 4 end style right parenthesis minus 1 right parenthesis left parenthesis left parenthesis begin display style 3 over 4 end style right parenthesis minus 2 right parenthesis left parenthesis left parenthesis begin display style 3 over 4 end style right parenthesis minus 3 right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative begin display style 6 over 4 end style plus 1 over denominator left parenthesis negative begin display style 1 fourth end style right parenthesis left parenthesis negative begin display style 5 over 4 end style right parenthesis left parenthesis negative begin display style 9 over 4 end style right parenthesis end fraction equals 2 over 45 space left parenthesis positif right parenthesis Untuk space 1 less than straight x less than 2 comma space pilih space straight x equals 3 over 2 space menjadi fraction numerator negative 2 straight x plus 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction equals fraction numerator negative 2 left parenthesis begin display style 3 over 2 end style right parenthesis plus 1 over denominator left parenthesis left parenthesis begin display style 3 over 2 end style right parenthesis minus 1 right parenthesis left parenthesis left parenthesis begin display style 3 over 2 end style right parenthesis minus 2 right parenthesis left parenthesis left parenthesis begin display style 3 over 2 end style right parenthesis minus 3 right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative begin display style 3 end style plus 1 over denominator left parenthesis begin display style 1 half end style right parenthesis left parenthesis negative begin display style 1 half end style right parenthesis left parenthesis negative begin display style 3 over 2 end style right parenthesis end fraction equals negative 4 over 3 space left parenthesis negatif right parenthesis Untuk space 2 less than straight x less than 3 comma space pilih space straight x equals 5 over 2 space menjadi fraction numerator negative 2 straight x plus 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction equals fraction numerator negative 2 left parenthesis begin display style 5 over 2 end style right parenthesis plus 1 over denominator left parenthesis left parenthesis begin display style 5 over 2 end style right parenthesis minus 1 right parenthesis left parenthesis left parenthesis begin display style 5 over 2 end style right parenthesis minus 2 right parenthesis left parenthesis left parenthesis begin display style 5 over 2 end style right parenthesis minus 3 right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative begin display style 5 end style plus 1 over denominator left parenthesis begin display style 3 over 2 end style right parenthesis left parenthesis begin display style 1 half end style right parenthesis left parenthesis negative begin display style 1 half end style right parenthesis end fraction equals 8 over 3 space left parenthesis positif right parenthesis Untuk space straight x greater than 3 comma space pilih space straight x equals 4 space menjadi fraction numerator negative 2 straight x plus 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction equals fraction numerator negative 2 left parenthesis begin display style 4 end style right parenthesis plus 1 over denominator left parenthesis left parenthesis begin display style 4 end style right parenthesis minus 1 right parenthesis left parenthesis left parenthesis begin display style 4 end style right parenthesis minus 2 right parenthesis left parenthesis left parenthesis begin display style 4 end style right parenthesis minus 3 right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative begin display style 8 end style plus 1 over denominator left parenthesis begin display style 3 end style right parenthesis left parenthesis 2 right parenthesis left parenthesis 1 right parenthesis end fraction equals negative 7 over 6 space left parenthesis negatif right parenthesis$

Maka garis bilangan menjadi :

Karena pertidaksamaan berbentuk “kurang dari” maka daerah yang dipilih adalah daerah negatif sehingga diperoleh penyelesaian: . Kemudian sesuai dengan opsi pada pilihan jawaban maka dipilih